Becky is a regional manager for two plants that put together light fixtures. The 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. Employees at the Denver plants can assemble 9 basic and 5 professional light fixtures each hour. To meet demand, Becky 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 workers 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 $4250 per week. She know she can probably schedule differently to reduce costs, but isn't sure how to go about it. Becky knows you are taking a class on optimizing profit and cost, so she's asked for your help with her recommendation. What recommendation should Becky make to the company CEO in order to minimize her cost but still meet demand? How much will this recommendation reduce labor cost?

Label and define the decision variables, objective function, and constraints. Clearly state the solution and answer all parts to the problem in complete sentences.