A sports goods manufacturer makes baseball and hockey gloves. Suppose now is the end of December and the manager wishes to plan production for the next three quarters. The forecast demand for aggregate units of pairs of gloves is: Q l: 9,400, Q2: 16,200, and Q3: 18,500. There are currently 26 permanent workers. Each worker works 480 hours a quarter and makes 1 pair of gloves per hour. The wage rate is $8 per hour, holding cost per unit per quarter is $ 1, and the backorder cost per unit per quarter is $10. The manager can hire fulltime temporary workers at the cost of $960 per person. Temporary workers also receive $8 per hour and work 480 hours a quarter. There is no layoff cost. Overtime by full-time workers is possible at 1.5 times the regular wage rate up to a maximum of 50 percent of regular time production. Current inventory level is zero and there is no inventory expected at the end of the planning horizon.
a. If 26 permanent worker’s are kept throughout the planning horizon, how many units will the company be short at the end?
b. Do tradeoff analysis to show that using temporary workers will be cheaper than using permanent workers during overtime,
c. Find the aggregate production plan that minimizes total cost.