QUESTION 2: Transportation Problem Formulation (16 points): BDM & Son's production manager is planning a series of monthly production schedules for its flagship noise cancelling headphones. The forecasted demand for the next three months is as follows: Month Demand for headphones 1 220 2 340 3 260 BDM & Son can normally produce 200 sets of headphones in a month. This is done during regular production hours at a cost of $500 per set of headphones. If demand in any month cannot be satisfied by regular production, the production manager has two other choices: (1) Each month a limited number of headphones can be purchased from a friendly competitor for resale (the maximum number of total outside purchases over the three-month period combined is 250 sets of headphones, at a cost of $350 each per set); (2) Alternatively, demand can be filled from on-hand inventory. The inventory carrying cost is $20 per set of headphones per month. Production from a given month can be used to satisfy demand in the following months. Back orders are not permitted (i.e., production in Month 2 cannot be used to meet demand from Month 1). Inventory on hand at the beginning of Month 1 is 25 sets of headphones. (i.e. beginning inventory in month 1 is 25 sets of headphones). Set up and formulate algebraically the above production scheduling problem as a TRANSPORTATION Model to minimize total cost over the planning period. Define the decision variables, objective function, and constraints. DO NOT SOLVE