It’s attached

OPRE.315.

Direction: Please show all work.

Points related to each problem are marked after

the problem number or problem part.

1. Consider the following linear programming problem

Min 8X1+9X2

s.t.

2X1 + X2  60

X1 + X2 8

X1, X2  0

1. Use a graph to show each constraint and the feasible region. Clearly identify the X1 and X2 value of each vertex.

X2

X1

1. Identify the optimal solution point on your graph. What are the values of X and Y at the optimal solution?

1. What is the optimal value of the objective function? What are the values of slack variables?

1. 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 28 hours of production time, and needs 15 units of foam backing.

The profit per roll of Grade X carpet is $200 and the profit per roll of Grade Y carpet is $160. In the coming production period, Muir has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1800 hours of production time (overtime is a possibility). The company has 1500 units of foam backing available for use. Develop and solve a linear programming model for this problem. Solve by Excel and attach only print out of the excel sensitivity output to this assignment.

Hint: Let X = the number of rolls of Grade X carpet to make

Let Y = the number of rolls of Grade Y carpet to make

A8

1. Formulate a liner programming problem in this situation.

1. How many rolls of Grade X carpet to make?

1. How many rolls of Grade Y carpet to make?

1. How many units of synthetic fiber is left over?

1. How many units of foam backing is left over?

1. What is the total profit?