Alice Ciccarelli, a landowner, has subdivided her 2,000 acre farm into three plots of varying sizes (i. e. 500, 900 and 600 acres). She has contracted with three local farm families (sharecroppers), assigning each of them to one of these plots, on the basis of their capabilities. Each sharecropper family will be instructed to plant one or more of three crops: corn, peas and soybeans, devoting a specific amount of acreage to each crop on its allocated plot. Any of the three crops can be planted on each of the three plots, but Alice has placed several restrictions on the farming operation. First, the maximum total acreage to be planted with corn, peas and soybeans are restricted to 9000, 700 and 1000, respectively. Furthermore, at least 60% of each plot must be cultivated and the same proportion of each plot should be under cultivation. Alice estimates that her per acre profit contributions for growing corn, peas and soybeans would be $550, $340 and $250, respectively. What instructions should Alice give to the sharecroppers? Required:
a. Formulate a linear programming model (i. e. clearly and completely define all decision variables, then construct the objective function and all constraints in algebraic format) for finding the optimal solution to Alice's farm operations.
b. Solve your model in part (a) using Excel/solver and clearly interpret the results.