Problem 1 [25'] A farmer owns two fields and he is currently planning agricultural production for the coming year. The agricultural output for each field is limited by the amount of available irrigable land and the quantity of water allocated for irrigation. Field Usable Land (Acres) Water Allocation 1 120 300 2 150 400 The crops suited for this region include corn and potato. These crops differ primarily in their expected net return per acre and their consumption of water. The first 100 acres planted for corn will have $100 per acre in net return and the remainder can only have $80 per acre in net return. The net return for potato is $75 per acre. Crop Maximum Quota (Acres) Water Consumption Corn 300 3 Potato 200 2 Due to the limitation of water available for irrigation, it is not possible to use all the irrigable land for planting crops. Moreover, due to the different soil conditions, he wants that field 2 to be planted with a proportion of its available irrigable land that is twice as field 1. For example, if field 1 plants 30 acres of its available 120 acres, then field 2 must plant 75 acres of its available 150 acres. However, any combination of the crops may be grown at any of the fields. The job is to plan how many acres to devote to each crop at the respective field while satisfying the given restrictions to maximize the total net return of the farm. (1) [15'] Formulate the problem to find a planting scheme that maximize the total net return of the farm as an LP model. Clearly define the decision variables, the objective function, and the constraints. (Hint: recall the model on lecture notes 2-23, if only the first 150 tables made can be sold at profit at $7 and the remainder can only be sold at a profit $2, then the objective function will become 7T - 5 max {T - 150, 0} + 5C, then you can introduce a new decision variable W = max{T - 150, 0} and reformulate the problem as a linear programming problem) (2) [10'] Solve the above LP model by Excel Solver and explain the optimal solution