Management Angela's Pizza is open from noon to midnight each day. Employees work 8-hour shifts from noon to 8 P.M. or 4 P.M. to midnight. The store manager estimates that she needs at least 5 employees from noon to 4 P.M., at least 14 employees from 4 P.M. to 8 P.M., and 6 employees from 8 P.M. to midnight. Employees are paid $5.50 per hour for hours worked between noon and 4 P.M. The hourly pay between 4 P.M. and midnight is $7.50.
a. Write inequalities to represent the number of day-shift workers, the number of night-shift workers, and the total number of workers needed.
b. Graph the system of inequalities.
c. Write a function to represent the daily cost of payroll.
d. Find the number of day-shift workers and night-shift workers that should be scheduled to minimize the cost.
e. What is the minimal cost?