Math 1324 Name Chapter 7 Lab 7.1-7.5 Instructions: Work each of the following problems in the space provided. You must show all work to receive full credit. Simplify and clearly indicate all answers. 1. You work at a department store that needs at least 4200 labor hours covered per week. It employs full- time staff 40 hours per week and part-time staff 25 hours per week. The cost to employ a full-time staff member is more because the company pays benefits such as health care and life insurance. Hours per Week Cost per Hour Full-time 40 hr $25 Part-time 25 h $18 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. You have been asked to help the store manager determine the number of full-time employees and the number of part-time employees that should be used to minimize the weekly labor cost. a. Clearly define the variables in this problem. * = hours per week 1 = cost per hour b. Clearly state the constraints (all inequalities) related to the feasible region. c. State the objective function. d. Use the graphical method to solve: Graph the solution region, showing the intercepts used. Label axes, units, points, and lines. Find and label all corner points. The grid for the graph is on the next page. Show all necessary work. e. In a complete sentence, state the number of full-time employees and the number of part-time employees that should be used to minimize the weekly labor cost