Linear Programming: Maximizing Beer Production

The production manager for Beer etc. produces two types of beer: light (L) and dark (D), using malt and wheat as resources. He is limited to at most 4800 oz of malt and 3200 oz of wheat per week. 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.

If the production manager decides to produce 0 bottles of light beer and 400 bottles of dark beer, he will consume 3,200 oz of malt and 3,200 oz of wheat. As he can obtain at most 4,800 oz of malt and 3,200 oz of wheat per week, there will be a slack of 1,600 oz of malt (4,800 - 3,200).

Therefore, the production manager will have a slack of malt only when producing 0 bottles of light beer and 400 bottles of dark beer. The consumption for malt is still less than the maximum allowed limit, while the consumption for wheat meets exactly the maximum allowed limit. This decision optimizes profits and resource utilization.