Johnny's apple shop sells home-made apple pies and freshly squeezed apple juice. Each apple pie requires 2 apples, and 1 apple yields 4 ounces of juice
Customer's use a self-service dispenser to pour apple juice in a container and are charged by the ounce at a rate of $0.50 per ounce. The contribution to profit of the apple pie, factoring in the apples and remaining ingredients are $2 per pie, and the contribution to profit of freshly squeezed apple juice if $0.20 per ounce. In a given day, there must be at least 100 ounces of apple juice produced and at least 10 apple pies. The company has a supply of 60 apples per day. Formulate this problem as a mixed integer program. Apple pies must be produced in whole quantities, but any positive value is positive for juice production.
Maximize: 0.2X1 + 2X2
Subject to: 0.25X1 + 2X2 ? 60
X1 ? 100
X2 ? 10
X2 must be integer
Where X1 = # of ounces of apple juice produced and X2 = # of apple pies produced
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