The seasonal yield of olives in a Piraeus, Greece, and 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 then permitting the olive grow on their own and result in a smaller size olive. It also, though, permits olive trees to be spaced closer together. They 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 780 hours of labor available and a total of 460 acres for growing. Because of the olive size difference, a barrel of olives produced on pruned trees sells for $ 42, whereas a barrel of regular olives has a market price of $ 30. The grower has determined that because of uncertain demand, no more than 80 barrels of pruned olives should be produced.
Use the graphical method to find.
(a)The maximum possible profit.
(b)The best combination of barrels of pruned and regular olives.
(c)The number of acres that the olive grower should devote to each growing process.