You have recently been hired as an operations research analyst in a consulting firm. Congratulations! The company now assigned you to work for Macrogames, which produces video games. The video game industry is highly volatile, and you are assigned to help them minimize the employment cost over the year. You may assume that no one quits or can be hired in the middle of a month. Month Macrogames currently estimates the total demand for labor hours over the next 12 months as given in Table 1. Table 1: Estimated demand over the next 12 months Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Anticipated demand in 7.2 6.5 3.7 4.6 7.3 9.5 9.9 thousands of hours 10. 6 5 10 9.3 5 Macrogames currently operates at 4 locations but is open to closing one of its locations. The maximum number of hours that any location can operate, the current number of employees, and the fixed cost to have a location open are given in Table 2. Table 2: Locations details Capacity of Labor Location hours a month Current number of employees (Dec.) Fixed cost (million $) New haven 4500 20 1.1 Newark 3900 15 1.5 New York City 3700 18 2.1 Boston 4000 16 1.7 Page 1 of 3 The company can hire new employees at any location at the beginning of each month. New employees need to be trained. Any employee that has finished training is capable of training a new employee. If an employee is training a new employee, he or she can only work at half the rate and should spend the rest of his or her time training the new employee. A normal employee who has been in the company for over a month will work 160 hours a month and receives $14 an hour (this includes benefits). Any employee who has been in the company for over a month can work overtime at 1.5 the pay rate, but each person is limited to at most 40 hours of overtime in any month. Any new employee who is in the training period will be paid $10 an hour, but the company cannot receive any benefit from such an employee. By union negotiations, any employee in the company has guaranteed pay for the complete 160 hours per month regardless of whether they are needed or not. If you fire an employee, you must pay them a month's salary of severance pay. Due to some varying tax laws, if the location at New Haven is open or closed, then Newark must also be open or closed. If New Haven and New York City are open and you have decided to close a location, then Boston must be closed. Either Newark or New York City must be open. Last year employment cost with similar demand was 8 million dollars and the company had a profit of $475,000. The company is hoping to go public in the next years and increasing the profit would be a substantial benefit to them