2. (60 points) A farmer grows corn and soybeans on two different small farms that he owns to produce feed for his livestock. Farm 1 is 10 acres in size and yields 184 and 65 bushels of corn and soybeans, respectively, per acre, while Farm 2 is 5 acres in size and yields 110 and 70 bushels of corn and soybeans, respectively, per acre. The total operating costs (e.g., fertilizer, seeds, fuel, insurance, labor, etc.) for planting one acre with corn and soybeans for Farm 1, is respectively $585 and $360, and for Farm 2, is respectively $490 and $290. The above information is summarized in the following table. 1 2 corn corn soybeans Farm Crop Operating Expenses ($/acre) Yield (bushels/acre) Land (acres) 585 184 soybeans 360 65 490 110 290 70 10 5 The farmer has further determined that the best feed for his livestock is a mixture of equal amounts (i.e., bushels) of corn and soybeans. (a) (40 points) Formulate the problem facing the farmer of how to plant crops of corn and soybeans on the two farms using all available acreage to achieve the livestock feed with the desired mixture of corn and soybeans at minimum cost as an LP. Clearly define the variables and describe the constraints in your formulation. (b) (20 points) To reduce his total operating costs, the farmer is willing to allow the difference between the amounts of the two crops produced to be as much as 10% of the total amount of feed produced. How would you modify your formulation in part (a) to model this flexibility