Problem 1 (Triangle Utilities) Triangle 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 shut-down 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 $6,000 for 1, $5,000 for 2, and $4,000 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.). Each generator can only be started once. All generators except the main generator are shut down at 10:00 p.m. Forecasts indicate the need for 3,200 megawatts more than provided by the main generator before 2:00 p.m., and this need goes up to 5,700 megawatts between 2:00 and 10:00 p.m. Generator 1 may provide up to 2,400 megawatts, generator 2 may provide up to 2,100 megawatts, and generator 3 may provide up to 3,300 megawatts. The cost per megawatt used per 8-hour period is $8 for 1, $9 for 2, and $7 for 3. (a) Formulate this problem as a mixed integer program to determine the least-cost way to meet the needs of the area. (b) Solve the problem formulated in (a) by Excel solver. Problem 2 (Football Game Program Sales) Every home football game for the past eight years at Eastern State University has been sold out. The revenues from ticket sales are significant, but the sale of food, beverages, and souvenirs has contributed greatly to the overall profitability of the football program. One particular souvenir is the football program for each game. The number of programs sold at each game is described by the following probability distribution: NUMBER (IN 100s) OF Probability PROGRAMS SOLD 23 24 25 26 27 0.17 0.2 0.23 0.21 0.19 Historically, Eastern has never sold fewer than 2,300 programs or more than 2,700 programs at one game. Each program costs $0.50 to produce and sells for $2.00. Any programs that are not sold are donated to a recycling center and do not produce any revenue. (a) Simulate the sales of programs at 10 football games. Specifically, start with creating the table of interval of random numbers for the demand distribution. Then, to generate the simulated demand numbers based on the table, use the last column in the random number table (found at the end of this document) and begin at the top of the column. (b) If the university decided to print 2,500 programs for each game, what would the average profits be for the 10 games simulated in part (a)? (c) If the university decided to print 2,600 programs for each game, what would the average profits be for the 10 games simulated in part (a)?