The seasonal yield of olives in a Piraeus Greece vineyard is

The seasonal yield of olives in a Piraeus, Greece, vineyard is greatly influenced by a process of branch pruning. If olive trees are pruned every two weeks, output is increased. The pruning process, however, requires considerably more labor than permitting the olives to grow on their own and results in a smaller size olive. It also, though, permits olive trees to be spaced closer together. The yield of 1 barrel of olives by pruning requires 5 hours of labor and 2 acres of land. The production of a barrel of olives by the normal process requires only 4 labor hours but takes 8 acres of land. An olive grower has 720 hours of labor available and a total of 580 acres for grow­ing. Because of the olive size difference, a barrel of olives produced on pruned trees sells for $40, whereas a barrel of regular olives has a market price of $33. The grower has determined that because of uncertain demand, no more than 50 barrels of pruned olives should be produced.

Use graphical LP to find:

(a) The maximum possible profit.

(b) The best combination of barrels of pruned and regular olives.

PLEASE PROVIDE STEP BY STEP SOLUTION

(c) The number of acres that the olive grower should devote to each growing process.

Solution