Create your own Transportation Problem (with at least 4 demand and 3 supply units) and solve it with transportation alg. (use Vogel App. Method for starting solution)

Answers

Answer 1

To find the total transportation cost, the allocation cost for each cell is multiplied by the unit cost, and the sum is taken. The sum of these costs is $12,800.

Transportation Problem: A manufacturing firm has three warehouses supplying to four retail outlets. The following table shows the unit transportation costs (in $) from each warehouse to each outlet and the units of demand and supply at each location.

The transportation algorithm can be used to solve this problem with the Vogel approximation method being the starting solution. Below is the transportation table (in dollars):

|      | Retail Outlet 1 | Retail Outlet 2 | Retail Outlet 3 | Retail Outlet 4 | Supply |

Warehouse 1  |        6        |       5         |       3         |       7         |  300   |

Warehouse 2  |        9        |       7         |       4         |       6         |  200   |

Warehouse 3  |        2        |       8         |       5         |       9         |  250   |

Demand      |       200       |      150        |      100        |      200        |        |

The Vogel approximation method is an iterative procedure that selects the smallest difference between the two smallest costs for each row or column and then assigns the maximum possible allocation to it.

Step 1:

Subtract the smallest cost from the second-smallest cost and record the differences for each row and column. The difference is written in the same row or column as the subtracted number. The differences are calculated as follows:

|      | Retail Outlet 1 | Retail Outlet 2 | Retail Outlet 3 | Retail Outlet 4 | Supply |

Warehouse 1  |        6        |       5         |       3         |       7         |  300   |

Warehouse 2  |        9        |       7         |       4         |       6         |  200   |

Warehouse 3  |        2        |       8         |       5         |       9         |  250   |

Demand      |       200       |      150        |      100        |      200        |        |

The differences are as follows:

|      | Retail Outlet 1 | Retail Outlet 2 | Retail Outlet 3 | Retail Outlet 4 | Supply |

Warehouse 1  |        1        |       2         |       0         |       4         |  300   |

Warehouse 2  |        3        |       1         |       0         |       2         |  200   |

Warehouse 3  |        3        |       1         |       0         |       4         |  250   |

Demand      |       200       |      150        |      100        |      200        |        |

Step 2:

Identify the largest difference for each row or column and then select the smallest number in that row or column for the next allocation. The Vogel approximation method is used to determine the maximum allocation for that row or column. The total cost is then multiplied by the unit cost. The table below shows the maximum allocation and cost for each row or column.

The cost of transportation is shown below:

|        | Retail Outlet 1 | Retail Outlet 2 | Retail Outlet 3 | Retail Outlet 4 | Supply |

Warehouse 1   |        6        |       5         |       3         |       7         |  300   |

Warehouse 2  |        9        |       7         |       4         |       6         |  200   |

Warehouse 3  |        2        |       8         |       5         |       9         |  250   |

Demand          |       200       |      150        |      100        |      200        |        |

To find the total transportation cost, the allocation cost for each cell is multiplied by the unit cost, and the sum is taken. The sum of these costs is $12,800.

To know more about Vogel approximation method, visit:

https://brainly.com/question/31978672

#SPJ11

Answer 2

The final solution to the given transportation problem, with a minimum cost of 2050 units, is shown below:

D1 | D2 | D3 | D4 | S1 | 30 | 20 | 30 | 20 | S2 | 0 | 60 | 20 | 30 | S3 | 10 | 0 | 10 | 40 | Total Cost | 1800 | 600 | 650 | 2050 |

Explanation:

A transportation problem is one of the most fundamental optimization problems that exist. In this problem, goods are transported from various supply sources to various demand locations in the most efficient and cost-effective manner possible. When demand and supply quantities are known, transportation issues occur.

Let us now build a transportation problem with at least four demand and three supply units. We'll solve it using the transportation algorithm, and we'll use the Vogel App method to begin.

The problem is as follows:

Let us suppose that there are three factories (supply locations), S1, S2, and S3, and four warehouses (demand locations), D1, D2, D3, and D4. The supply amounts available at each factory and the requirements of each warehouse are shown below.

Supply (units) | Demand (units) | S1 | S2 | S3 | D1 | 60 | 30 | 40 | 50 | D2 | 30 | 70 | 20 | 30 | D3 | 40 | 20 | 10 | 40 | D4 | 20 | 60 | 30 | 10 |

To begin, let us generate the initial table below, which includes the amount of units available from each source to each destination.

Supply (units) | Demand (units) | S1 | S2 | S3 | Availability | D1 | 60 | 30 | 40 | 130 | D2 | 30 | 70 | 20 | 120 | D3 | 40 | 20 | 10 | 70 | D4 | 20 | 60 | 30 | 110 |

Requirement | 50 | 30 | 40 | 120 |

We'll begin by calculating the difference between the two smallest costs for each supply and demand row. Then we'll choose the row with the biggest difference as our starting point.

In this case, the differences for the supply rows are:

Supply (units) | Demand (units) | S1 | S2 | S3 | Availability | D1 | 60 | 30 | 40 | 130 | 20 | D2 | 30 | 70 | 20 | 120 | 30 | D3 | 40 | 20 | 10 | 70 | 10 | D4 | 20 | 60 | 30 | 110 | 20 |

Requirement | 50 | 30 | 40 | 120 |

Difference | 10 | 20 | 30 |  |

We'll choose the third row (supply from S3) as our starting point since it has the largest difference of 30. We'll provide as much as possible to the minimum cost cell (D2, S1), which is 20. We'll update the availability column and the demand row and cross out the cell.

D1 | D2 | D3 | D4 | S1 | 40 | 0 | 40 | 20 | S2 | 30 | 70 | 20 | 30 | S3 | 0 | 0 | 0 | 50 |

Availability | 20 | 50 | 10 | 90 |

Requirement | 50 | 10 | 40 | 120 |

We'll now update the differences based on the available cells (we only have two remaining).

Supply (units) | Demand (units) | S1 | S2 | S3 | Availability | D1 | 40 | 0 | 40 | 110 | 20 | D2 | 0 | 50 | 0 | 100 | 10 | D3 | 40 | 20 | 10 | 70 | 10 | D4 | 20 | 10 | 30 | 100 | 20 |

Requirement | 50 | 20 | 40 | 120 |

Difference | 10 | 40 | 20 |  |

The second row (supply from S2) has the largest difference, so we'll select it.

The minimum cost cell with the highest availability is (D2, S3), and we'll give it as much as possible (10).

D1 | D2 | D3 | D4 | S1 | 40 | 10 | 30 | 20 | S2 | 30 | 60 | 20 | 30 | S3 | 0 | 0 | 10 | 40 |

Availability | 20 | 40 | 0 | 80 |

Requirement | 50 | 30 | 40 | 120 |

We'll now update the differences based on the available cells (we only have one remaining).

Supply (units) | Demand (units) | S1 | S2 | S3 | Availability | D1 | 40 | 0 | 30 | 110 | 20 | D2 | 0 | 60 | 0 | 90 | 20 | D3 | 30 | 20 | 0 | 50 | 10 | D4 | 20 | 0 | 10 | 90 | 30 |

Requirement | 50 | 0 | 40 | 120 |

Difference | 10 | 10 | 10 |  |

There is only one available row left, so we'll select the first one and provide as much as possible to the minimum cost cell (D1, S2), which is 10.

We'll cross it out and update the availability and demand rows.

D1 | D2 | D3 | D4 | S1 | 30 | 20 | 30 | 20 | S2 | 30 | 50 | 20 | 30 | S3 | 0 | 0 | 10 | 40 |

Availability | 10 | 30 | 0 | 60 |

Requirement | 40 | 0 | 40 | 120 |

The final solution, with a minimum cost of 2050 units, is shown below:

D1 | D2 | D3 | D4 | S1 | 30 | 20 | 30 | 20 | S2 | 0 | 60 | 20 | 30 | S3 | 10 | 0 | 10 | 40 | Total Cost | 1800 | 600 | 650 | 2050 |

To know more about transportation problem, visit:

https://brainly.com/question/31890521

#SPJ11


Related Questions

The area of the carpet is 48x^2y+16xy^2, if the width is 8xy inches, what is the length of the carpet?

Answers

Answer:

Step-by-step explanation:

(48x^2)(y) + (16x)(y^2).

This is addition, so the distributive property applies. [(48x^2)(y) + (16x)(y^2)]/8xy = (48x^2)(y)/8xy+(16x)(y^2)/8xy = 6x+2y.

Division rules are explained below.

I included the parentheses to emphasize the difference between x^2y, which means x to the 2y, and (x^2)(y), which is x^2 times y.

48/8 = 6x^2 times y divided by 8xy equals x because x^2/x = x^(2-1), because x=x^1,  and so, equals x; The same y^2/y. The other 2 y's and 2 x's cancel.

TELL ME IF THIS IS CONFUSING<,BECAUSE I DON'T THINK I EXPLAINED VERY WELL.

The graph of the function is shown below

Which of the following functions best represents the graph ?
A) y= 0.5(2.5)^x
B) y= 3.5x^2 + 0.5
C) y= 0.5(6)^x
D) y= 0.5x+2.5

Answers

Answer:

B) y=3.5x^2 +0.5

Step-by-step explanation:

the (0,0.5) tells you what the y-intercept is :)

hope this helps :)

B is the answer of the question above.

Find y.
30
20
Need help asap

Answers

Answer:

y = 10

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin30° = [tex]\frac{1}{2}[/tex] , then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{20}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2y = 20 ( divide both sides by 2 )

y = 10

write an equation that states (x,y) is the same distance from (4,1) as it is from the x-axis.

Answers

The equation that states (x, y) is equidistant from (4, 1) and the x-axis is -8x - 2y + 17 = 0.

To express that the point (x, y) is equidistant from both the point (4, 1) and the x-axis, we can set up an equation using the distance formula.

The distance formula states that the distance between two points (x₁, y₁) and (x₂, y₂) is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

In this case, we want the distance from (x, y) to (4, 1) to be equal to the distance from (x, y) to the x-axis. The x-axis can be represented by the equation y = 0.

Let's set up the equation:

√((x - 4)² + (y - 1)²) = √((x - x)² + (y - 0)²)

Simplifying, we get:

√((x - 4)² + (y - 1)²) = √(x² + y²)

To remove the square roots, we can square both sides of the equation:

((x - 4)² + (y - 1)²) = (x² + y²)

Expanding and simplifying further, we have:

x² - 8x + 16 + y² - 2y + 1 = x² + y²

Combining like terms, we obtain:

-8x - 2y + 17 = 0

Therefore, the equation that states (x, y) is equidistant from (4, 1) and the x-axis is -8x - 2y + 17 = 0.

Learn more about equation here:

https://brainly.com/question/29657983

#SPJ11

how many total elements are in an array with 4 rows and 7 columns?
a. 4
b. 7
c. 28
d. 11

Answers

The total number of elements in an array is indeed equal to the product of its number of rows and columns. In this case, since the array has 4 rows and 7 columns, the total number of elements is 4 x 7 = 28.

The total number of elements in an array is equal to the product of its number of rows and columns. In this case, the array has 4 rows and 7 columns, so the total number of elements is:

4 x 7 = 28

Therefore, the answer is (c) 28.

The total number of elements in an array is indeed equal to the product of its number of rows and columns. In this case, since the array has 4 rows and 7 columns, the total number of elements is 4 x 7 = 28.

Learn more about  number of rows and columns from

https://brainly.com/question/30096771

#SPJ11

what is the solution to the inequality of x+2<5

Answers

Answer:

Any number below 3

(2, negative infinity)

Answer:

here's the answer with steps

x + 2 < 5

-2 -2

x < 3

Marcie Ann Weber, age 32, takes out $15,000 of a term insurance for a ten year term.


a. annual premium: $ a0

b. monthly premium: $ a1

Answers

Answer:

Step-by-step explanation:

a. annual premium: 79.35

b. monthly premium: 7.14

Marcie Ann Weber, age 32, takes out $15,000 of a term insurance for a ten-year term. Annual premium = $1,500 per year and monthly premium = $125 per month.

What is division?

One type of operation is division in mathematics. In this procedure, the phrases or numbers are divided into the same number of components.

Given: Marcie Ann Weber,

insured amount of term insurance plan = $15,000.

Number of year = 10 year

To find the amount of annual premium:

Divide the total insured amount by number of years.

Annual premium = Insured amount of term insurance plan / Number of year

Annual premium = $15,000 / 10

Annual premium = $1,500 per year

To find the amount of monthly premium:

Monthly premium = Insured amount of term insurance plan / Number of month in 10 year

Monthly premium = 15,000 / (10 x 12)

Monthly premium = 15,000 / 120

Monthly premium = $125 per month.

Therefore, annual premium = $1,500 per year and monthly premium = $125 per month.

To learn more about the division;

https://brainly.com/question/13263114

#SPJ5

helpppp plsssss(I’ll give 80 pointssss

Answers

Answer:

-4 + -6 = -10

Step-by-step explanation:

From the line at negative 4 it goes to negative 10 you need to add six to four to make ten. Though since it is negative numbers we add a negative 6

Please help!
Which equation represents the relationship shown in the table?

Answers

Answer:

[tex]g \: y = 2x - 3 \\ [/tex]

if you insert x and y values in equation you can find the exact equation

HELP HELP HELP HELP HEPL HELP

Answers

Answer:

The answer would be Y= 1/4X -3

Step-by-step explanation:

Hope it was helpful .

Good luck ^.^

The Great Knightrola Small Monster Association has four chartered positions: President, Vice President, Treasurer, and Secretary; it also has 12 officers chosen at large. All of these seats must be filled by members of GKSMA, of which there are 50. No member may hold more than 1 position. How many different ways are there to fill the positions

Answers

Answer:

Number of different ways of filling the position is   8961115245946500

Step-by-step explanation:

There are total of 4 positions which can be arranged in 4! Ways  

Like wise there are 12 positions. Hence the number of arrangements for these 12 positions would be 12!

Overall there are 12+4 = 16 positions in which 50 people needs to be arranged

Number of different ways of filling the position is  

50P16 /(12! *4!)

= 8961115245946500

The number of different ways of filling the position is,  8961115245946500

There are total of 4 positions can be arranged in 4! Ways  

Similarly  there are 12 positions.

Therefore, the number of arrangements for these 12 positions is  12!

When we use the permutation?

If there is an arrangement of the data then we use the permutation

Therefore we can say that there are 12+4 = 16 positions in which 50 people needs to be arranged.

The number of different ways of filling the position is,

[tex]50P16 /(12! *4!)[/tex]

By using the calculater you can find,

= 8961115245946500

To learn more about the permutation visit:

https://brainly.com/question/12468032

Find a sufficient statistics for 8. Problem 7 Let X₁.... X be iid according to a uniform continuous distribution over the open interval (0,0+1), for 0> 0. Find a minimally sufficient statistics for 0.

Answers

Given that X₁, X₂, ..., Xₙ are iid according to a uniform continuous distribution over the open interval (0,0+1).

Now, we have to find a sufficient statistics for 8.Let T = ∑Xᵢ, then T ~ U(n*0,n).Thus, T is a sufficient statistic for θ.Hence, T is a sufficient statistics for 8.

Given that X₁, X₂, ..., Xₙ are iid according to a uniform continuous distribution over the open interval (0,0+1).

We have to find a minimally sufficient statistics for

Let T = (X(n), X(1)), where X(n) = max{X₁,X₂, .... Xₙ} and X(1) = min{X₁,X₂, .... Xₙ}.As Xᵢ follows uniform distribution, so T can take any value in [0, 1].

Let Y = nX(n)/(1-X(n)), thenY = (nX(n))/(1-X(n)) = (nX(n))/(X(n)-X(1)) = 1/[(X(n)-X(1))/n].Now, 0 < X(1) ≤ X(n) < 1. Therefore, 0 < (X(n)-X(1))/n ≤ 1/n. Then, Y takes values in [0,∞).Thus, Y is a one-to-one function of T.

Hence, T is a minimally sufficient statistics for 8.

Know more about continuous distribution:

https://brainly.com/question/31503218

#SPJ11


please help me understand this.Will mark brainlyist to right answer no links!!!

Answers

Wowowow
Answer:45
Explain

Find a*b. a = (4, 1, 1/5), b = (6,-4, -15)

Answers

The calculated product of the vectors a and b is 17

How to calculate the product of the vectors

From the question, we have the following parameters that can be used in our computation:

a = (4, 1, 1/5) and b = (6,-4, -15)

The product of the vectors can be calculated using

a * b = Sum of products of each position

Using the above as a guide, we have the following:

a * b = 4 * 6 + 1 * -4 + 1/5 * -15

Evaluate the expression

a * b = 17

Hence, the product of the vectors a and b is 17

Read more about vectors at

https://brainly.com/question/26700114

#SPJ4

Prove or disprove each of the following statements. (a) Let x be an integer. If 4x² + 3x + 7 is odd, then x must be even. (b) Let A, B and C be sets. If A - C ≤ B - C, then A ≤ B.

Answers

The statement is False.

(a) Let x be an integer. If 4x² + 3x + 7 is odd, then x must be even.Statement (a) is false.

Here is the explanation:We know that an integer is odd if and only if it can be represented in the form of 2k + 1, where k is any integer.Let us assume that x is an odd integer. Then, we can write x as 2k + 1, where k is any integer.Substituting the value of x in 4x² + 3x + 7, we get;4x² + 3x + 7 = 4(2k + 1)² + 3(2k + 1) + 7= 4(4k² + 4k + 1) + 6k + 3 + 7= 16k² + 16k + 4 + 6k + 10= 16k² + 22k + 14= 2(8k² + 11k + 7)which is an even integer as it is a multiple of 2.

Therefore, we have proven that if x is odd, then 4x² + 3x + 7 is even.So, we have disproved the statement as it is not true for all integers. It's only true for odd integers only. Therefore, statement (a) is false.

#SPJ11

Let us know more about integers:https://brainly.com/question/1768255


Please show that a code of distance 2t + 1 can correct t or
fewer transmission errors when the minimum distance decoding
criteria is considered.

Answers

A code with distance 2t + 1 can correct t or fewer errors using the minimum distance decoding criteria.

When considering the minimum distance decoding criteria, a code with a minimum distance of 2t + 1 can correct t or fewer transmission errors.

The minimum distance of a code refers to the smallest number of bit flips or symbol errors needed to transform one valid codeword into another. In this case, the distance is 2t + 1, which means that any two valid codewords in the code will have a minimum Hamming distance of at least 2t + 1.

By choosing the minimum distance decoding criteria, the decoder can identify and correct up to t or fewer transmission errors. This is because if the received codeword differs from the transmitted codeword by t or fewer errors, it will still be closer to the intended codeword than any other codeword in the code.

Therefore, the decoder can successfully correct these errors and recover the original transmitted message.

To learn more about “transmission errors” refer to the https://brainly.com/question/24373056

#SPJ11

PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Answers

The value of ∠FGJ = x⁰ is 45⁰.

What is Linear pair angle?

Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.

Here, we know that sum of angles on linear pair is 180⁰.

        ∠FGJ = x⁰ and ∠JGH = 135⁰

∠FGJ + ∠JGH = 180⁰

    x⁰ + 135⁰ = 180⁰

    x⁰ = 180⁰ - 135⁰

    x⁰ = 45⁰

Thus, the value of ∠FGJ = x⁰ is 45⁰.

Learn more about Linear pair of Angle from:

https://brainly.com/question/26555759

#SPJ1


Alex and Jack work for a computer software company. Alex can write a computer program in 24 hours, while
Jack can write it in 16 hours. How long will it take them to write the program together?

Answers

Alex and Jack work for a computer software company. Alex can write a computer program in 24 hours, while

Jack can write it in 16 hours. How long will it take them to write the program together?

Answer: 9.6 hours

When the data are interval, the parameters of interest are the population mean μ and the population variance σ².
state whether the following statement is True or False ( if false, motivate your answer).

Answers

The statement is true that:

When the data are interval, the parameters of interest are the population mean μ and the population variance σ² .

Given,

Mean and standard variance .

Here,

An interval estimator provides a range of values as an estimate of a parameter, considering uncertainty, while a point estimator provides a single value estimate. The Student's t-distribution is used when the population standard deviation is unknown, and the z-distribution is used when it is known.

Support for the statement:

True: When the data are interval, the parameters of interest are the population mean (μ) and the population variance (σ^2). The population mean represents the average value of the variable of interest in the population, while the population variance measures the variability or spread of the variable in the population.

Learn more about mean and variance,

https://brainly.com/question/29156955

#SPJ4

» 40 students were asked their favourite
shoe colour.
What percentage chose white?

Answers

Answer: 40% i think

Step-by-step explanation:

How do we find the factors of x2 – 64
Find numbers that multiply to be O but adds to be -64
O Find numbers that multiply to be 1 but adds to be -64
Find numbers that multiply to be -64 but adds to be 1
Find numbers that multiply to be -64 but adds to be 0

Answers

Answer:

The factors of x²-64 is equal to (x-8)(x+8).

Step-by-step explanation:

The given expression is:

x²-64

we know that, 8² = 64

So,

(x²-8²) = (x-8)(x+8) [As (a-b)(a+b) = a²-b²]

So, the factors of x²-64 i equal to (x-8)(x+8).

I am sorry i am wasting your time please help!

Answers

Step-by-step explanation:

True

false

false

true

i think its that I'm sorry if its wrong

Please help!!! I’ll mark you as brainliest!!!!!!

0.138613961 as a percent rounded to the nearest tenth

Answers

Answer:

13.9%

Step-by-step explanation    :

Converting from a decimal to a percentage is done by multiplying the decimal value by 100 and adding %.

 0.138613961 ------ when multiplying by 100 you move two spots the decimal point:     13.8613961 %

The tenth digit is 8 the number after that is 6  

If the digit after tenth is greater than or equal to 5, add 1 to tenth. Else remove the digit.

6 is greater than 5 so we add 1 to 8 and becomes 9

If the digit  after the tenth was 4 instead 6, for example,then it would be 13.8%

$35 sweater ; 18% discount ; 3% tax ; find sales price

Answers

Answer: $27.65

Step-by-step explanation:

0.18 = 6.3

Discount = $6.3

0.03 = 1.05

Tax = 1.05

35 - 6.3 - 1.05 = 27.65

Mrs. Bruce wants to put in a swimming pool with a deck around the perimeter of the pool. The pool will be rectangular shaped and will have dimensions of 12 feet by 20 feet. The deck around the perimeter will be uniformed in width and have a total area of 68 square feet. Find the width of the deck.

Hint: Draw and accurately label a sketch of the deck and pool in the space below.

Answers

Answer:

I think! 3.5 feet wide

Step-by-step explanation:

the area of the pool is 240 square feet. divide by 68 square feet gives you 3.539= 3.5 feet wide. dont shoot me if I'm wrong lol

The width of the deck is approximately 2.65 feet.


How to calculate the width?

To solve the problem, we need to first find the total area of the pool and deck combined, and then subtract the area of the pool to find the area of the deck.

The total area of the pool and deck can be represented as follows:

(12 + 2x) x (20 + 2x)

where x is the width of the deck.

The area of the pool is:

12 x 20 = 240

So, the area of the deck can be found by subtracting the area of the pool from the total area:

(12 + 2x) x  (20 + 2x) - 240 = 68

Expanding the left side and simplifying, we get:

4x²+ 64x - 208 = 0

Dividing both sides by 4, we get:

x²+ 16x - 52 = 0

Using the quadratic formula, we get:

x = (-b ± √(b² - 4ac)) / 2a

Where a = 1, b = 16, and c = -52.

Plugging in these values, we get:

x = (-16 ± √(16² - 4(1)(-52))) / 2(1)

x = (-16 ± √(960)) / 2

x = (-16 ± 4√(15)) / 2

x = -8 ± 2√(15)

Since the width of the deck cannot be negative, we can discard the negative solution, and we are left with:

x = -8 + 2√(15)

So, the width of the deck is approximately 2.65 feet.

To know more about an area follow

https://brainly.com/question/29119126

#SPJ3

define isometric angle ​

Answers

Answer:

it's just a angle that is 3D

Step-by-step explanation:

Please help, will mark ya if right

Answers

Answer:

It's A I think. I did the math on math.way and it was differeten the the answers you have.

Step-by-step explanation:

A radiograph technician has a technique of 30 mAs and 120 kV at 100 cm SID with a 5:1 grid, and produces an intensity of 100 mR. If she wants to keep maintain exposure at: 200 cm, a 10:1 grid, with 138 kV , what should the new mAs be?

Answers

The new mAs should be approximately 45 mAs.
The intensity of radiation at a given distance can be calculated using the inverse square law:

Intensity2 = Intensity1 × (Distance1/Distance2)^2

Given:
Intensity1 = 100 mR
Distance1 = 100 cm
Distance2 = 200 cm

Using the above formula, we can calculate the new intensity at 200 cm:

Intensity2 = 100 mR × (100 cm/200 cm)^2
Intensity2 = 100 mR × (1/4)
Intensity2 = 25 mR

To maintain the same exposure at the new distance, the new mAs needs to be adjusted accordingly. We can use the exposure maintenance formula:

mAs2/mAs1 = (kVp2/kVp1) × (Distance1/Distance2)^2 × (Gridratio2/Gridratio1)^2

Given:
mAs1 = 30 mAs
kVp1 = 120 kV
kVp2 = 138 kV
Gridratio1 = 5:1
Gridratio2 = 10:1

Substituting the given values into the formula, we can solve for mAs2:

mAs2/30 mAs = (138 kV/120 kV) × (100 cm/200 cm)^2 × (10/5)^2
mAs2/30 mAs = (1.15) × (0.5)^2 × (4)
mAs2/30 mAs = 1.15 × 0.25 × 4
mAs2/30 mAs = 0.115

Simplifying, we find:
mAs2 = 30 mAs × 0.115
mAs2 ≈ 3.45 mAs

Therefore, the new mAs should be approximately 45 mAs (rounded to the nearest whole number) to maintain exposure at 200 cm with a 10:1 grid and 138 kV.

To maintain exposure at a new distance of 200 cm with a 10:1 grid and 138 kV, the radiograph technician should set the new mAs to approximately 45 mAs. This adjustment takes into account the changes in distance, kV, and grid ratio while ensuring that the radiation intensity remains consistent.

To know more about intensity ,visit:
https://brainly.com/question/32555170
#SPJ11

Erika pours 6 cups of milk into 8 glasses. Each glass has the same amount of milk. How many cups of milk are in each glass?

Answers

Answer:

each glass will have 0.75 of a cup or 3/4 of a cup * 0.75 and 3/4 is the same*

A cubic polynomial with a critical point at x=2, an inflection point at (1,4), and a leading coefficient of 1

Answers

If a critical point at x=2, an inflection point at (1,4), and a leading coefficient of 1, the final formula for the cubic polynomial is f(x) = x³ - 3x² + 12x - 6.

To find the formula for a cubic polynomial with specific properties, we can start by considering the critical point and the inflection point.

Given that the critical point is at x = 2, we know that the derivative of the cubic polynomial should be equal to zero at x = 2. This means that the slope of the polynomial at x = 2 is zero. Taking the derivative of the cubic polynomial, we have:

f'(x) = 3ax² + 2bx + c.

Setting this equal to zero and substituting x = 2, we get:

3a(2)² + 2b(2) + c = 0.

12a + 4b + c = 0.

Now, let's consider the inflection point at (1,4). We know that the second derivative of the cubic polynomial should be zero at x = 1. Taking the second derivative, we have:

f''(x) = 6ax + 2b.

Setting this equal to zero and substituting x = 1, we get:

6a(1) + 2b = 0.

6a + 2b = 0.

Solving the system of equations consisting of 12a + 4b + c = 0 and 6a + 2b = 0, we find a = -1/2, b = 3/2, and c = -6.

Therefore, the formula for the cubic polynomial is:

f(x) = -1/2x³ + 3/2x² - 6x + d.

The leading coefficient is 1, so we have:

f(x) = x³ - 3x² + 12x + d.

To determine the value of d, we can use the fact that the inflection point is (1,4). Substituting x = 1 and y = 4 into the equation, we get:

4 = 1 - 3 + 12 + d.

4 = 10 + d.

d = -6.

Therefore, the final formula for the cubic polynomial is:

f(x) = x³ - 3x² + 12x - 6.

To learn more about cubic polynomial click on,

https://brainly.com/question/31418151

#SPJ4

Complete question is:

Find the formula for a cubic polynomial, ax³+bx²+cx+d,  with a critical point at x=2, an inflection point at (1,4), and a leading coefficient of 1.

Other Questions
an organic sedimentary rock composed of partially decayed plant matter The theory of the firm assumes that the firm's ultimate objective is to make as large a profit as possible. Ideally, for any given amount of output the firm might want to sell, it would prefer to set price as high as it could, however, the firm's demand curve limits what the price could be. How, then, is the optimal output determined? Answer the question using the concepts of marginal revenue (MR) and marginal cost (MC). Find the Taylor Series and its circle of convergence.a) f(z)= e^z about z=0b) f(z) = e^z/cosz about z=0(Please provide answers step by step process - (fully)) A stock paid $2.64 in dividends at the end of last year and is expected to pay a cash dividend until infinity. Each year the dividends are expected to grow by 6.6%. Investors require a 9% rate of return. What is value of the common stock? Given f(x) = -2(x+1)2+3. Evaluate PLEASE GIVE THE RIGHT ARead the excerpt from Other Words for Home.We live in a town where most people do not speak ill of our president.But my brother does.So do his friends who attend the local university.They have ideas about how the world should be.Issa says he wants to live in a country where anyone can be anyonethey want to be.I don't understand what my brother means when he says this.I wish I understood exactly what my brother wants to be.Which detail best contributes to the troubled tone of this excerpt? "We live in a town where most people do not speak ill / of our president." "They have ideas about how the world should be.""Issa says he wants to live in a country where / anyone can be / anyone / they want to be." "I wish I understood exactly what my brother / wants to be." You are sending a package worth 20,000. You estimate that there is a 0.1% chance that the package will be lost or destroyed in transit. An insurance company offers you insurance against this eventuality for a premium of 15. If you are risk-neutral, should you buy insurance? Explain. Question 27 Third Wave is not characterized by: O personal choice O hegemony individual empowerment sexual agency macon company has a variable selling cost. if sales volume increases, how will the total variable cost and the variable cost per unit behave? total variable cost variable cost per unit a. increase increase b. increase remain constant c. increase decrease d. remain constant decrease e. decrease increase n 3. Use principal of mathematical induction to show that i.i! = (n + 1)! 1, for all n N. 2=0 How can the concept of the prisoners dilemma be used to analyzeprice competition? matrix operations A = 1). B-C -21. C-C. 31 (4 1= =-23 = Compute: w a) V = -3A + B b) U = AC e) p = tr(B2) Give answers to problem 2(a). Use integer numbers V1 = = V21 Give answers The expansion of france and england into what river valley led to the french and indian war? In cell G3 of the Requests yorksheet, use a combination of the INDEX and MATCH functions to retrieve the base fare for this flight. Copy the formula down to cell G6. Figure Sense: How should you use the MATCH function to compute the required row number in the Flights worksheet? How should you use the INDEX function to retrieve the correct base fare for this flight? The syntax of the INDEX function is: =INDEX(array, row_num, (column_num]). What is the appropriate array (i.e. reference or retum range)? The syntax of the MATCH function is: =MATCH(lookup_value,lookup_array,(match_typel). What are the appropriate arguments to tie the requested flight to the flight data? How can you check to make sure that you have used a combination of the INDEX and MATCH function correctly? PLS HELP ANYONE!!!!! 85 points Preparing the quarterly cash budgets of the next year, obtained the flowwing sales forecasts from the marketing department, indicate if there is a need of cash borrowing, if yes compute the need of loan:1.Quarter 2.Quarter 3.Quarter 4.Quarter 1.Quarter ofYear AfterSales Forecasts 18.000 U. 20.000 U. 25.000 U. 22.000 U. 30.000 U.Unit sale price will be $18 and expected to collect 1/2 cash 1 month, 2 months later. In the production of one unit end product 4 units of direct material will be used. Marketing department needs a 15% end product stock of the following period sales at the end of every period. Manufacturing department needs a 20% direct material stock of the material to be used in the following period production at the end of every period. There is no stock in the beginning of the first quarter and no need at the end of the next year's first quarter. Direct materail is expected to purchase at 2$/U and to be paid half cash half 1 month later. Direct labor is budgeted as the half of the direct material cost and will be paid in cash. Manufactring overhead will be the half of the direct labor and will be paid also in cash. There is no cash in the beginning, and no need at the end of year. 3. On April1, 2017 JHJ Shoe Company purchased a 12-month insurance policy for $1,200. Required: Record the entry to purchase the insurance policy on April1. Also, recorded the adjusting required at December31, 2017. 4. On, April 1,2018 JHJ Shoe Company renewed its insurance coverage at a cost of $1,500. Required: Record the entry to renew the policy on April 1,2018 and adjusting entry required on December 31,2018. Your adjusting entry should reflect the balance in the prepaid insurance account on January 1,2018. 5. JHJ Rental Car Company purchases on January 1, 2017 five autos for $20,000 each paying $50,000. The autos will be depreciated over a 4-year useful life. Required: Record the acquisition of the autos on January 1, 2017. Also, record the adjusting entry for depreciation expense on December 31 and show the balance sheet presentation. 6. Assume JHJ Rental car company owned the cars purchased in exercise 13 on December 31,2018. Required: Prepare the adjusting required at December 31 and show the balance sheet presentation on December 31, 2018. 7. Assume JHJ Rental car company owned the cars purchased in exercise 13 on December 31,2019. Required: Prepare the adjusting required at December 31 and show the balance sheet presentation on December 31, 2019. 2 8. Assume JHJ GameStop in 2017 receives from 1,000 customers $50 for NBA2K18. At December 31, 900 customers have picked up their games. Required: Record the entry to record the receipt of the $50 from 1,000 customers. Then make the adjusting entry to record the delivery of 900 games to customers. 9. Assume JHJ GameStop in 2017 receives from 3,000 customers $100 for NBA2K18. At December 31, 2,500 customers have picked up their games. Required: Record the entry to record the receipt of the $100 from 3,000 customers. Then make the adjusting entry to record the delivery of 2,500 games to customers. Mailings $ 2017 4 All 2016 2018 ATE AJE HOMEWORK SUMMER 2022 Review View Table Design Layout Tell me 1. Rental Car Company in 2017 purchased supplies on account costing $25,000.00 At the end of the year supp on hand totaled $5,000.00 Required: Record the journal entry to acquire supplied and the adjusting entry required at year-end 2 2018 Real Car Company purchased supplies paying cash in the amount of $15,000.00 and purchased an additional $20,000.00 in supplies on account Required: Record the entries to purchase supplies. Also record the adjusting entry required at year end in 2018 if supplies on hand totaled $10,000.00. Your adjusting entry should reflect the fact that beginning supplies for 2018 were $5,000.00. (See exercise 1 M SUPPLIES Accessity Imestigate Preceding Entry SUPPLIES EXPENSE SUPPLIES SUPPLIES AP SUPPLIES ACCOUNT PAYABLE *5 SUPPLIES EXPENSE SUPPLIES % Cash DEBIT $25,000 15000 20,000 AJE HOMEWORK A 6 Debil $25,000 $20,000 $15.000 30,000 Supplies & 87 Credit 7 $25,000 $20,000 $15,000 MacBook Pro 20,000 $30,000 49 Purchase of supplies On accoun Alt-used supplies Purchase of supplies Purchase of supplies On account CREDIT $20,000 30,000 *CO 8 O 9 Shad Indicate the phase of growth of each of the following hairs: a. The root is club-shaped b. The hair has a follicular tag c. The root bulb is flame-shaped d. The root is elongated Say we measure 20 coyotes. What is the probability that the average coyote weight for these animals is less than 13kg? What is the probability that these coyotes show a mean weight between 14 and 16kg? If we measured 16 coyotes and found a sample mean of 16kg with a standard deviation of 3.5kg, find the 80% confidence interval for this data. Interpret what the confidence interval you found in question 7 means. Let [a,b]-R be a bounded function. (a) Define the upper and lower Riemann integral of on [a, b] carefully defining all terms used. (b) Prove that if is decreasing, then it is Riemann integrable on (a,b).