The production manager for Beer etc. produces two kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. The manager 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.
-Which of the following is not a feasible solution?
A) 0 L and 0 D
B) 0 L and 400 D
C) 200 L and 300 D
D) 300 L and 200 D

Question

Quizplus · Accepted Answer

We can use linear programming to find the optimal solution. Let:
- x = number of bottles of light beer
- y = number of bottles of dark beer
Then we want to maximize profit: 
Maximize 2x + y
Subject to:
- 12x + 8y ≤ 4800 (malt constraint)
- 4x + 8y ≤ 3200 (wheat constraint)
- x, y ≥ 0 (non-negativity constraint)
Simplifying the constraints, we get: 
- 3x + 2y ≤ 1200
- x + 2y ≤ 800
The feasible solution set is the intersection of the non-negativity constraint with the region bounded by these two lines and the axes (see graph below).

A) 0 L and 0 D: This is a feasible solution, but not an optimal one as the profit is 0. 
B) 0 L and 400 D: This is a feasible solution, as it satisfies all constraints. The profit is 400. 
C) 200 L and 300 D: This is a feasible solution, as it satisfies all constraints. The profit is 800. 
D) 300 L and 200 D: This is not a feasible solution, as it violates the malt constraint: 12(300) + 8(200) = 5600 > 4800. 
Therefore, the best choice(s) is/are:
Answer: C
 The optimal solution is to produce 200 bottles of light beer and 300 bottles of dark beer, which gives a profit of $800.

The Production Manager for Beer Etc