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. Employees 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 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 $$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 MAT$218$ and have learned about optimizing profit and cost, so she's asked for your help with her recommendation for how to schedule hours at the plants in order to minimize cost.

Question $11$

How many hours should be scheduled at the Phoenix plant to minimize cost?

Question $12$

How many hours should be scheduled at the Denver plant to minimize cost?

Question $13$

What is the minimum cost $($in dollars$)$ according to the new schedule you determined?

Question $14$

How much $($in dollars$)$ will the cost be reduced if the CEO follows the solution you found?

Question $15$

What recommendation should Shay make to the company CEO in order to minimize cost but still meet demand?