The production manager for Beer etc. produces 2 kinds of beer: light (L) and dar

Q: The production manager for Beer etc. produces 2 kinds of beer: light (L) and dar

Decision variables: l, d be the number of bottles of light and dark beer produced respectively Constraints: 4l+8d

ID: 469237 • Letter: T

Question

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 12 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. If the production manager decides to produce of 0 bottles of light beer and 400 bottles of dark beer, it will result in slack of A) malt only B) wheat only C) both malt and wheat D) neither malt nor wheat Write the formulation for this linear program And Explain

Explanation / Answer

Decision variables:

l, d be the number of bottles of light and dark beer produced respectively

Constraints:

4l+8d<=3200

12l+8d<=4800

l, d>=0

Objective function:

Maximize (2l+1d)

Solving in Solver:

Inequalities in Linear programming are converted into equalities by introducing slack variables. In the case of 0 light beers and 400 dark beers:

As we can see, the LHS and RHS of supply constraint for wheat is equal, hence no slack, but in Malt supply constraint, LHS value, 3200 is less than equal to RHS value of 4800, hence if the manager decides to produce 0 bottles of light beer, and 400 bottles of dark beer, it will result in slack of a) Malt only.