Good evening,

Need help with the following problems ASAP. Thank you for your help.

Problem 1

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 then 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 6 hours of labor and 3 acres of land. The production of a barrel of olives by the normal process requires only 5 labor hours but takes 10 acres of land. An olive grower has 360 hours of labor available and a total of 290 acres for growing. Because of the olive size difference, a barrel of olives produced on pruned trees sells for $32, whereas a barrel of regular olives has a market price of $40. The grower has determined that because of uncertain demand, no more than 38 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.

Problem 2

Consider the following LP problem.

Max profit = 4X + 7Y

Subject to 0 3X + 4

(a) What is the optimal solution to this problem? Solve it graphically.

(b) If a technical breakthrough occurred that raised the profit per unit of X to $9, would this affect the optimal solution?

(c)Instead of an increase in the profit coefficient X to $9, suppose that profit was overestimated and should only have been $2. Does this change the optimal solution?