Consider the following problem and solve it using stochastic programming via Python+Gurobi (or pulp). You grow wheat, corn, and sugar beet on 500 acres of land. Planting an acre costs $150, $230, and $260, respectively. Need 200t of wheat and 240t of corn for cattle feed. Excess production of wheat and corn is sold at $170/t and $150/t; however, if less is produced, it is bought at $238/t and 210/t, respectively. Sugar beet sells at $36/t below 6000t, and sells at $10/t above 6000t (laws courtesy of the European Commission) The average yields of crop are: 2.5t/acre for wheat, 3t/acre for corn, and 20t/acre for beet. Depending on how good the weather is, these yields may decrease or increase by 20%. That is, there are three scenarios with equal probability: high yield, average yield, and low yield (i.e. discrete scenario). How to solve this problem and maximize total profit? You should decide how many acres to use for each crop.

(a) (5%) Define decision variables and give linear programming (LP) formulation with respect to average yield scenario (i.e. EV solution).

(b) (5%) Solve the solution of Scenario Analysis and the EV solution?