Chapter 8.6, Problem 26PE

A large department store needs at least $3600$ labor hours covered per week. It employs full-time staff $40\text{ hr/wk}$ and part-time staff $25\text{ hr/wk}\text{.}$ The cost to employ a full-time staff member is more because the company pays benefits such as health care and life insurance.

The store manager also knows that to make the store run efficiently, the number of full-time employees must be at least $1.25$ times the number of part-time employees.

a. Determine the number of full-time employees and the number of part-time employees that should be used to minimize the weekly labor cost.

b. What is the minimum weekly cost to staff the store under these constraints?