Midlife Shoes, Inc. is a manufacturer of sensible shoes for aging baby-boomers. The company is having great success, and although demand is seasonal, it is expected to increase steadily over the next few years. The company is purchasing a new facility to accommodate the increase in demand, but the facility will not open until 13 months from now. The current facility can only accommodate 15 workers. Hiring and firing costs are negligible. Using the information below, help Midlife manage this transition year by deriving a production plan that will meet demand at the lowest cost. With the limited workforce size, neither chase demand nor level production is viable.
Month Demand
January .......1000
February .......1200
March ........1200
April ..........3000
May ........3000
June ........3000
July .........2200
August .......2200
September .......4000
October ........4000
November .......2200
December ........3000
Beginning inventory 0 units
Beginning workforce 8 workers
Production rate 100 units per worker per month
Regular capacity Maximum of 15 workers
Overtime capacity Half of regular production
Subcontracting capacity 1000 units
Regular production cost $36 per unit
Overtime production cost $54 per unit
Subcontracting cost $70 per unit
Inventory holding cost $10 per unit