Determining the production of corn and tobacco

Question

Problems:

 x1 = no. of acres of corn

 x2 = no. of acres of tobacco

maximize             Z = 300x₁+520x₂

Subject to:                 x₁+x₂≤410

                              105x₁+210x₂≤52,500

                                         x₂≤100    

                                         x₁,x₂≥0

a) Solve this graphically by providing the extreme points and the corresponding z-values. Indicate the optimum solution.

b) How many acres of farmland will not be cultivated at the optimal solution? Do the Bradleys use the entire 100-acre tobacco allotment?

c) What would the profit for corn have to be for the Bradleys to plant only corn?

d) If the Bradleys can obtain an additional 100 acres of land, will the number of acres of corn and tobacco they plan to grow change?

e) If they decide not to cultivate a 50-acre section as part of a crop recovery program, how will it affect their crop plans?