The production manager for Beer Inc produces two kinds of be

The production manager for Beer Inc. produces two kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer requires 8 oz of malt and 8 oz of wheat.

Profits for a bottle of light beer are $2 per bottle, and a profits for a bottle of dark beer are $1 per bottle.

How many bottles of light beer should the company produce to maximize its weekly profit?

Solution

It\'s a linear programming optimization problem

maximize

2L + D
Subject to
L = 12M + 4W
D = 8M + 8 W
M < 4800
W < 3200
M=1/8(2L-D)<4800

W=1/16(3D-2l)<3200

The ponit we have choose that

(0,400), (400,0), (0,0), and (300,200)

For these point, the weekly profit is maximize when

L=300, D=200

2*300+1*200=800