Muir Manufacturing produces two popular grades of commercial carpeting among its

Question

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. Formulate the problem as a linear program. Solve the problem using graphical solution. Develop an Excel Spreadsheet model for this problem and solve.

Explanation / Answer

Answer to the question 1: Formulate LPP:

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

Objective: Maximize Profit 200X + 160Y
Input Constraints:
50S + 25P + 20F = X(Synthetic fiber)
40S + 28P + 15F = Y (Production time)
S<=3000
P>=1800
F<=1500

We can reformulate the above as:
Objective: Maximize Profit 200(50S + 25P + 20F) + 160(40S + 28P + 15F)
Input Constraints:
S<=3000
P>=1800
F<=1500

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