# Linear and Sensititive Analysis

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The solution converts this linear problem into excel using solver and shows the sensititive analysis.

10. Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade X carpet uses 50 units of synthetic fiber, requires 25 hours of production time, and needs 20 units of foam backing. Each roll of Grade Y carpet uses 40 units of synthetic fiber, requires 30 hours of production time, and needs 15 units of foam backing.

The profit per roll of Grade X carpet is $180 and the profit per roll of Grade Y carpet is $150. In the coming production period, Muir has 3000 units of synthetic fiber available for use. There is 1800 hours of production time available. The company has 1500 units of foam backing available for use.

a. State the problem as a linear program on a sheet of paper

b. Solve the linear program in Excel.

c. What is the value of the objective function?

d. What are the binding constraints?

e. How much would the profit increase if another 100 units of synthetic fiber

were made available?

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##### Solution Summary

The solution converts this linear problem into excel using solver and shows the sensititive analysis.

10. Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade X carpet uses 50 units of synthetic fiber, requires 25 hours of production time, and needs 20 units of foam backing. Each roll of Grade Y carpet uses 40 units of synthetic fiber, requires 30 hours of production time, and needs 15 units of foam backing.

The profit per roll of Grade X carpet is $180 and the profit per roll of Grade Y carpet is $150. In the coming production period, Muir has 3000 units of synthetic fiber available for use. There is 1800 hours of production time available. The company has 1500 units of foam backing available for use.

a. State the problem as a linear program on a sheet of paper

b. Solve the linear program in Excel.

c. What is the value of the objective function?

d. What are the binding constraints?

e. How much would the profit increase if another 100 units of synthetic fiber

were made available?

##### Solution Preview

The solution converts this linear problem into excel using solver and shows the sensititive analysis.

10. Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Muir needs to decide how many rolls of each grade should be ...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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