AGRICULTURE. BP Farms is a 300-acre farm located near Lawrence, Kansas, owned and operated exclusively by Bill Pashley. For the upcoming growing season, Bill will grow wheat, corn, oats, and soybeans. The following table gives relevant data concerning expected crop yields, labor required, expected pre harvested expenses, and water required (in addition to the forecasted rain). Also included is the price per bushel Bill expects to receive when the crops are harvested.

Bill wishes to produce at least 30,000 bushels of wheat and 30,000 bushels of corn, but no more than 25,000 bushels of oats. He has $25,000 to invest in his crops, and he plans to work up to 12 hours per day during the 150-day season. He also does not wish to exceed the base water supply of 1200 acre-feet allocated to him by the Kansas Agriculture Authority.

a. Formulate the problem for BP Farms as a linear program and solve for the optimal number of acres of each crop Bill should plant in order to maximize his total expected return from the harvested crops.

b. If the selling price of oats remains $1.45 a bushel, to what level must the yield increase before oats should be planted? If the yield for oats remains 180 bushels per acre, to what level would the price of oats have to rise before oats should be planted?

c. If there were no constraint on the minimum production of corn, would corn be planted? How much would the profit decrease if corn were not grown? d. La Mancha Realty owns an adjacent 40-acre parcel, which it is willing to lease to Bill for the season for $2000. Should Bill lease this property? Why or why not?