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Profit Maximization

Allie grows apples and sells two products, boxes of apples and jugs of apple cider. Allie has capacity constraints of three kinds: warehouse space, crating facilities, and pressing facilities. A box of apples requires 6 units of warehouse space, 2 units of crating facilities, and no pressing facilities. A jug of apple cider requires 3 units of warehouse space, 2 units of crating facilities, and 1 unit of pressing facilities. The total amounts available each day are: 1200 units of warehouse space, 600 units of crating facilities, and 250 units of pressing facilities.

a) If the only capacity constraint were on warehouse space (the other two facilities were of unlimited supply), and if all warehouse space were used for the production of boxes of apples, how many boxes could be produced in one day? How many jugs could be produced in one day if all warehouse space were used for the production of jugs of apple cider, and there were no other capacity constraints? Draw a line in a graph to represent the warehouse space constraint on production combinations.

b) How many boxes of apples could be produced in one day if Allie only had to worry about crafting capacity and no other constraints? How many jugs of apple cider?

Draw another line on the same graph of (a) to represent the crafting capacity constraint on production combinations.

c) How many boxes of apples could be produced in one day if Allie only had to worry about pressing capacity and no other constraints? How many jugs of apple cider?

Draw another line on the same graph of (a) to represent the pressing capacity constraint on production combinations.

d) Now identify the area that represents feasible combinations of daily production of boxes of apples and jugs of apple cider for Allie.

e) Allie can sell apples for $5 per box, and cider for $2 per jug. Solve for Allie’s revenue maximization problem. What is Allie’s optimal production plan? What is the maximum revenue?