There are two power plants generating electricity, and three factories that need electricity in their production. The demand for each factory, the capacity of each power plant, and the transmission costs per MWatt (S) are given in the following tables: PP1 PP2 Capacity (MWatt) 1250 2000 F1 F2 F3 Demand (MWatt) 1500 1300 1750 PP2 Cost(S/MWatt) F1 PP1 50 30 F2 F3 45 60 35 20 Note that total power plant capacity is insufficient to cover total demand of all factories. The penalty cost of unmet demand at F1, F2 and F3 is $120/MWatt, $115/MWatt and $128/MWatt, respectively. a. Formulate the linear programming model that minimizes the total cost. b. Solve the LP model using the MS Excel solver. Write down the optimal values of the decision variables and the optimal objective function value. Provide your Excel sheet, answer report, and sensitivity report.