36 The size of the yield of olives in a vineyard is greatly influenced by a process of branch pruning. If olive trees are pruned, trees can be planted more densely, and output is increased. (However, olives from pruned trees are smaller in size.) Obtaining a barrel of olives in a pruned vineyard requires 5 hours of labor and 1 acre of land. Obtaining a barrel of olives by the normal process requires only 2 labor hours but takes 2 acres of land. A barrel of olives produced on pruned trees sell for $20, whereas a barrel of regular olives has a market price of $30. An olive grower has 250 hours of labor available and a total of 150 acres available to plant. He has determined that because of uncertain demand, no more than 40 barrels of pruned olives should be produced.

Find the combination of barrels of pruned and regular olives that will yield the maximum possible profit. Also, how many acres should the olive grower devote to each growing process?

Note: Problems 37 to 43 are straightforward extensions of the two-variable problems we have seen so far and involve more than two variables. They therefore cannot be solved graphically. They are intended to give you an excellent opportunity to get familiar with formulating larger LP problems and solving them using Excel.