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LP to maximize profit for a brewery

The production manager for Beer etc. produces 2 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 per week respectively. Each bottle of light beer requires 16 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle.
Formulate a linear programming model for this problem.
What is the optimal weekly profit?
100
200
400
600
800

How many bottles of light beer should the company produce in order to maximize weekly profit?
100
200
300
400
500

How many bottles of dark beer should the company produce in order to maximize weekly profit?
0
100
200
300
400

What is the shadow price for Malt?
0
0.125
0.250
0.375
0.5

Solution Preview

Student, see attached Excel which has the LP model in the Solver tab and these answers highlighted, found using Excel Solver with "Linear Model" and "Assume Nonnegative" checked on ...

Solution Summary

Attached Excel has the LP model in the Solver tab and the answers highlighted, found using Excel Solver with appropriate options dialog selections. The shadow price is extracted from the Sensitivity Report tab)

$2.19