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.
How many rolls of Grade X & Grade Y should be produced to maximize profits?

Answer 1

Answer:

With 16 Grade X and 54 Grade Y the company maximize their profit at 11,840 dollars

Explanation:

We set up the scenario in Excel and use SOLVER tool:

X = 50 synthetic + 25 labor + 20 foam

Y = 40 synthetic + 28 labor + 15 foam

Profit:

X = 200

Y = 160

Constraing:

synthetics <= 3,000

foam <= 1,500

Grade X and Grade Y are integer.

goal: maximize profit

16 of Grade X

and 54 of grade Y

16 x 50 = 800

16 x 30  = 540

54 x 40  = 2,160

54 x 15  =    810

Profit:

16 x 200 + 54 x 160 = 11840