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Question 2: Mathematical programming and spreadsheet model (25 marks) An electrical utility needs to generate at least 5000 megawatts of electricity today using five generators. If any electricity is generated by a given generator, that generator must be started up and a fixed start-up cost is incurred. There is an additional cost for each megawatt generated by a generator. These costs, as well as the maximum capacity of each generator, are shown in the table below. The electricity generated by Generator 3 must be at least 1000 megawatts greater that of Generator 2. The objective is to determine the minimum cost plan that meets the constraints. Generator Fixed start-up cost Cost per megawatt/day generated Maximum capacity (MW/day) 1 $1000 $3 2500 2 $2000 $4 3000 3 $2500 $6 2000 4 $3000 $5 1500 5 $1500 $3 1600 a. Write the mathematical model. (15 marks) Solve it using Excel solver. (10 marks) b. Instruction: To write a mathematical model, you need to do the followings: Define the decision variables and parameters (if they are shown by math symbols). %20 Write the objective function and constraints. The objective function and constraints in the mathematical model should be numbered. %60 Explain each line of the mathematical model after the model by referring to its number. %20 To Solve a mathematical model using Excel solver, the following parts should be done: Report each formula you have used in a cell of your spreadsheet model together with its address. For example, G8=SUMPRODUCT(C8:F8,C11:F11). %20 Report a screenshot of your spreadsheet model that has been solved and the optimal solution can be seen in it. Use meaningful labels in your spreadsheet model. %60 Report the screenshot of the solver window that has been filled out completely. %20