Would overtime production by permanent workers and regular time production by temporary workers simultaneously result in a lower total cost?

MT makes small camping and snowmobile trailers. The demand for camping trailers occurs between January and June (mostly in April and May). MT makes camping trailers from January to June, shuts down in July and then makes snowmobile trailers from August to November. Suppose now is the end of December. For simplicity, we consider every two months as a period. The forecasts for camping trailers during each of the next three periods (six months) are:

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MT employs 40 permanent workers who are paid an average of $20 per hour (including fringe benefits) and work approximately 320 hours a period (2 months). They make approximately 1,000 camping trailers per period during regular time. They can also work up to 50 percent more as overtime (i.e., up to 12 hours a day vs. the regular 8 hours a day) and will be paid 1.5 times the regular wage rate. Alternatively, MT can hire up to 40 additional temporary workers to work during a second shift. Hiring cost is $3,000 per temporary worker. Assume temporary workers’ wage rate and productivity are the same as permanent workers. Also assume that temporary workers work only during regular time (no overtime) and are kept for whole periods (i.e., for 2 months or 4 months). Inventory holding cost per camping trailer per period is $180 and is charged to average inventory level during each period. Currently there are no camping trailers on hand, and the desired inventory at the end of period 3 is zero (although a small positive number is also acceptable). MT wishes to meet the total demand, but shortage during a period (except last) is acceptable, in which case the shortage is assumed to be backordered at the cost of $600 per camping trailer per period.

a. Calculate all the relevant unit costs.

b. Suppose MT uses permanent workers during regular time and overtime. Determine the minimum cost plan in this case. Hint: Use overtime in each period.

c. Suppose MT hires temporary workers but decides not to use permanent workers during overtime (just regular time). Determine the minimum cost plan in this case. Hint: Hire 15 temps for two periods and 9 temps for 1 period starting in period 2.

d. Would overtime production by permanent workers and regular time production by temporary workers simultaneously result in a lower total cost? Complete a tradeoff analysis. What is the overall minimum cost plan?

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