Question: Beth's Broasted Chicken shop offers a variety of fast-food items. Beth uses regular and part-time workers to meet demand. The demand for the next 12 months has been forecast in thousands of dollars, as follows:
Assume that each employee can produce $5000 worth of demand in a month. The company pays regular workers $10 per hour, including benefits, and part-time workers $7 per hour. There are 167 working hours in a month. Management would like to use as many part time workers as possible but must limit the ratio to one regular worker to no more than one part-time worker to provide adequate supervision and continuity of the workforce. A fractional number of part-time workers (e.g., 2.6 workers) can be employed since less than a full day of employment is possible for each worker. For example, if 10.6 total workers are needed, 6 regular workers and 4.6 part-time workers is a feasible combination, but 5 regular workers and 5.6 part-time workers is not, because the part-time workers exceed the fulltime workers. Demand cannot be inventoried and must be met on a month-by-month basis. It costs $500 to hire and $200 to lay off a regular worker. No costs are associated with hiring and laying off part-time workers.
a. Develop a strategy for this problem by using the minimum integer number of regular workers along with the maximum amount of part-time workers in each month. What is the total cost of this strategy including regular time labor, part-time labor and hiring/firing cost?
b. What is the total cost of a strategy with a constant level of 6 full-time workers used in each month?
Excess labor is allowed when demand is less than six full-time workers.