PROBLEM 2: [25 points] An electrical utility needs to generate 6,500 megawatts (MW) of electricity today. It has five generators available. If a given generator makes any electricity, that generator must be started and a fixed start-up cost is incurred. There is an additional cost for each MW generated by a generator. These costs, as well as the maximum capacity of each generator, are shown in the following table. A generator can generate any number of MWs between 0 and its maximum capacity. The objective is to determine the minimum cost plan that meets the electrical needs for today. Fixed start-up cost Cost per megawatt generated Maximum capacity (MW) 1 $3000 $5 2100 Generator 2 3 4 $2000 $2500 $1500 $4 $6 $6 1800 2500 1500 5 $1000 $7 3000 (a) Formulate the problem in mathematic form; clearly define variables, objective and constraints. (You do not need to solve it) [16 points] (b) Suppose that there is a constraint that at most 3 of the 5 of the generators may be run at the same time." Express a mathematical formulation of this constraint. [3 points] (c) Suppose that there is a constraint that generator 2 cannot be run if generator 5 is run. Give a mathematical formulation of this constraint.[3 points] (d) Suppose that there is a constraint that generator 2 may be run only if generator 5 is run." Give a mathematical formulation of this constraint. [3 points]