Question: Shadow prices-land management for Problem refer to the farm co-op application in Example. Rework that linear programming problem with the indicated changes in one constraint and answer the questions.
Example: A farm co-op has 6000 acres available to plant with corn and soybeans. Each acre of corn requires 9 gallons of fertilizer/herbicide and 3/4 hour of labor to harvest. Each acre of soybeans requires 3 gallons of fertilizer/herbicide and 1 hour of labor to harvest. The co-op has available at most 40,500 gallons of fertilizer/herbicide and at most 5250 hours of labor for harvesting. If the profits per acre are $60 for corn and $40 for soybeans, how many acres of each crop should the co-op plant to maximize their profit? What is the maximum profit?
(a) If one more acre of land became available (for a total of 6001 acres), how would this change the co-op's planting strategy and its maximum profit?
(b) Repeat part (a) if 8 more acres of land were available.
(c) Based on parts (a) and (b), what is the profit value of each additional acre of land? This value is called the shadow price of an acre of land.