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.

Fixed start-up cost Cost per megawatt/day generated Maximum capacity (MW/day) 1 $1000 $3 2500 2 $2000 $4 3000 Generator 3 $2500 $6 2000 4 $3000 $5 1500 5 $1500 $3 1600 a. Write the mathematical model. (15 marks) b. Solve it using Excel solver. (10 marks)