Byron's Manufacturing makes tables. Demand for the next four months and capacities of the plant are shown in the table below. Unit cost on regular time is $40. Overtime cost is 150% of regular time cost. Subcontracting is available in substantial quantity at $75 per unit. Holding costs are $5 per table per month; back orders cost the firm $10 per unit per month. Byron's management believes that the transportation algorithm can be used to optimize this scheduling problem. The firm has 50 units of beginning inventory and anticipates no ending inventory.
| | March | April | May | June |
| Demand | 400 | 600 | 600 | 700 |
| Regular capacity | 400 | 400 | 400 | 400 |
| Overtime capacity | 100 | 100 | 100 | 100 |
| Subcontract cap. | 150 | 50 | 50 | 50 |
a. How many units will be produced on regular time in June?
b. How many units will be produced by subcontracting over the four-month period?
c. What will be the inventory at the end of April?
d. What will be total production from all sources in April?
e. What will be the total cost of the optimum solution?
f. Does the firm utilize the expensive options of subcontracting and back ordering? When; why?
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