1. (18 points) Your friend Shay is a regional production manager responsible for two plants that assemble light fixtures. The company CEO has asked her to make a recommendation to reduce the labor cost of the production lines at the two plants she manages to help improve the financial situation of the company. Her plants (located in Phoenix and Denver) assemble both basic light fixtures for residential homes and professional light fixtures for business office spaces. Employees at the Phoenix plant can assemble 6 basic and 4 professional light fixtures each hour. Em- ployees at the Denver plant can assemble 9 basic and 5 professional light fixtures each hour. To meet demand, Shay knows that she must produce at least 1000 of each type of light fixture each week. Labor at the Phoenix plant costs $15 per hour. Labor at the Denver plant costs $20 per hour. She currently schedules work- ers at the Phoenix plant for 150 hours per week and workers at the Denver plant for 100 hours per week for a total labor cost of $4,250 per week. She knows she can probably schedule differently to reduce costs, but isn't sure how to go about it. Shay knows you are taking MAT218 and have learned about optimizing profit and cost, so she's asked for your help with her recommendation. What recommendation should Shay make to the company CEO in order to minimize her cost but still meet demand? How much will this recommendation reduce labor cost? Set up this problem by hand and use Excel to solve it. As part of your set up, you should include clearly labeled and defined decision variables, objective func- tion, and constraints. Remember to clearly state the solution to all parts to the problem in one or more complete sentences. 1. (18 points) Your friend Shay is a regional production manager responsible for two plants that assemble light fixtures. The company CEO has asked her to make a recommendation to reduce the labor cost of the production lines at the two plants she manages to help improve the financial situation of the company. Her plants (located in Phoenix and Denver) assemble both basic light fixtures for residential homes and professional light fixtures for business office spaces. Employees at the Phoenix plant can assemble 6 basic and 4 professional light fixtures each hour. Em- ployees at the Denver plant can assemble 9 basic and 5 professional light fixtures each hour. To meet demand, Shay knows that she must produce at least 1000 of each type of light fixture each week. Labor at the Phoenix plant costs $15 per hour. Labor at the Denver plant costs $20 per hour. She currently schedules work- ers at the Phoenix plant for 150 hours per week and workers at the Denver plant for 100 hours per week for a total labor cost of $4,250 per week. She knows she can probably schedule differently to reduce costs, but isn't sure how to go about it. Shay knows you are taking MAT218 and have learned about optimizing profit and cost, so she's asked for your help with her recommendation. What recommendation should Shay make to the company CEO in order to minimize her cost but still meet demand? How much will this recommendation reduce labor cost? Set up this problem by hand and use Excel to solve it. As part of your set up, you should include clearly labeled and defined decision variables, objective func- tion, and constraints. Remember to clearly state the solution to all parts to the problem in one or more complete sentences