Reference no: EM132264827

Quant Utilities provides electricity for three cities. The company has four electric generators that are used to provide electricity. The main generator operates 24 hours per day, with an occasional shutdown for routine maintenance. Three other generators (1, 2, and 3) are available to provide additional power when needed. A start-up cost is incurred each time one of these generators is started. The start-up costs are $9,000 for 1, $3,000 for 2, and $7,000 for 3. These generators are used in one of the following ways: a generator may be started at 6:00 a.m. and run for either 8 hours or 16 hours, or it may be started at 2:00 p.m. and run for 8 hours (until 10:00 p.m.). All generators except the main generator are shut down at 10:00 p.m. Forecasts indicate the need for 5,100 megawatts more than provided by the main generator before 2:00 p.m., and this need goes up to 6,300 megawatts between 2:00 and 10:00 p.m. Generator 1 may provide up to 2,300 megawatts, generator 2 may provide up to 2,400 megawatts, and generator 3 may provide up to 3,650 megawatts. The cost per megawatt used per 8-hour period is $5 for 1, $7 for 2, and $4 for 3. (a) List your decision variables and clearly write down what they represent. Note that, for example, if you just list your variables in a format of x1 = ads, x2 = TV, you will get 0 points. (b) Formulate this problem mathematically to determine the least-cost way to meet the needs of the area. That is, write your objective function subject to constraints. Note that it is your responsibility to decide if a decision variable is continuous, integer, or binary. (c) Solve the problem using Excel Solver. (d) Write down the decision indicating the variable solutions and the optimal objective value. (This is expected to be done similar to how I do in class. Failing to response properly will lead to 0 points)