How do I find the two variables and what is the objective function?

Question

The employees of a warehouse work 8-hour shifts. There are two different shifts the employees can work, the day shift from 8AM to 4PM or the second shift from 2PM to 10PM. Employees earn $11.50 per hour for the day shift and $13 for the second shift. The day shift must have at least 35 employees and the second shift must have at least 25 employees. For the overlapping time, from 2PM to 4PM, there must be at least 65 employees working. Write the objective function and constraints that model the given situation, then graph. How many day shift and second shift employees should be scheduled to optimize labor costs?

Answer 1

Let F= Number of First Shift workers. and S = Number of Second shift worker. Total labor cost (the objective function we are looking to maximize is

TC= 11.5F +13S subject to F>=35, S>=25 and F+S>=65