0.2 0.5 0.3 Problem The board of directors at a power company need to determine the optimal capacity investment in various types of power plants so as to meet the next-period demand for electricity. At the time of the decision, the next-period demand is unknown and may vary according to three different scenarios specified in the table below. Scenarios Next-period demand (MWh) Probability High demand 86,400 Medium demand 72,000 Low demand 57,600 To meet the demand, the board of directors are considering investment in four different types of power plants where the cost per unit of capacity installed for plant type 1, 2, 3, and 4 is $10M, $8M, $8M, and $6M, respectively. There is a total budget of $65M for capacity installment. Each installed unit of power plant type 1, 2, 3, and 4 can operate in one of three different modes during the next period, which can be decided upon later once the demand is realized. The energy output and the cost per unit operating level of each power plant type in different modes for the next period are as follows: Energy Output Per Unit Installed (in MWh) Plant type 1 Plant type 2 Plant type 3 Plant type 4 13,000 11,000 8,000 5,000 Mode 2 10,500 9,500 6,000 3,000 Mode 3 9,000 7,500 4,000 2,000 Model Mode 1 Mode 2 Mode 3 Plant type 3 M 2.4 M 0.4 M Operating Cost Per Unit Installed in dollars) Plant type 2 Plant type 3 4.5 M 3.2 M 2.7 M 1.9 M 0.42 M 0.32 M Plant type 4 3.2 M 2 M 0.55 M a) Formulate a two-stage stochastic program to help the board of directors determine how many units of each power plant type to install in order to meet the next-demand period. Assume fractional units are allowed. Specify the decision variables at each stage, the constraints, and the objective function. b) Solve your formulation using Microsoft Excel Solver and report the optimal values for the investment and operational variables. 0.2 0.5 0.3 Problem The board of directors at a power company need to determine the optimal capacity investment in various types of power plants so as to meet the next-period demand for electricity. At the time of the decision, the next-period demand is unknown and may vary according to three different scenarios specified in the table below. Scenarios Next-period demand (MWh) Probability High demand 86,400 Medium demand 72,000 Low demand 57,600 To meet the demand, the board of directors are considering investment in four different types of power plants where the cost per unit of capacity installed for plant type 1, 2, 3, and 4 is $10M, $8M, $8M, and $6M, respectively. There is a total budget of $65M for capacity installment. Each installed unit of power plant type 1, 2, 3, and 4 can operate in one of three different modes during the next period, which can be decided upon later once the demand is realized. The energy output and the cost per unit operating level of each power plant type in different modes for the next period are as follows: Energy Output Per Unit Installed (in MWh) Plant type 1 Plant type 2 Plant type 3 Plant type 4 13,000 11,000 8,000 5,000 Mode 2 10,500 9,500 6,000 3,000 Mode 3 9,000 7,500 4,000 2,000 Model Mode 1 Mode 2 Mode 3 Plant type 3 M 2.4 M 0.4 M Operating Cost Per Unit Installed in dollars) Plant type 2 Plant type 3 4.5 M 3.2 M 2.7 M 1.9 M 0.42 M 0.32 M Plant type 4 3.2 M 2 M 0.55 M a) Formulate a two-stage stochastic program to help the board of directors determine how many units of each power plant type to install in order to meet the next-demand period. Assume fractional units are allowed. Specify the decision variables at each stage, the constraints, and the objective function. b) Solve your formulation using Microsoft Excel Solver and report the optimal values for the investment and operational variables