11 Consider the following LP:

The optimal solution to this LP is z = 9, x1 = 1, x2 = 6.
Graphically find the range of values of b2 for which the current basis remains optimal.
12 Farmer Leary grows wheat and corn on his 45-acre farm. He can sell at most 140 bushels of wheat and 120 bushels of corn. Each planted acre yields either 5 bushels of wheat or 4 bushels of corn. Wheat sells for $30 per bushel, and corn sells for $50 per bushel. Six hours of labor are needed to harvest an acre of wheat, and 10 hours are needed to harvest an acre of corn. As many as 350 hours of labor can be purchased at $10 per hour. Let A1 =acres planted with wheat A2 = acres planted with corn L = hours of labor that are purchased To maximize profits, farmer Leary should solve the following LP:

Use the LINDO output in Figure 13 to answer the following questions:
a What is the most that Leary should pay for an additional hour of labor?
b What is the most that Leary should pay for an additional acre of land?
c If only 40 acres of land were available, what would be Leary’s profit?
d If the price of wheat dropped to $26, what would be the new optimal solution?
e Farmer Leary is considering growing barley. Demand for barley is unlimited. An acre yields 4 bushels of barley and requires 3 hours of labor. If barley sells for $30 per bushel, should Leary produce any barley?

Transcribed Image Text:

max z=3x1 + x2 s.t. 2x1 + x28 4x1 + x2 10 X1, X20