Please provide all detaile and formula. Please do not forget provide answers for (c) and (d).

MT is a manufacturer of small camping and snowmobile trailers. The demand for camping trailers occurs between January and June of each year (mostly in April and May). MT makes camping trailers during 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 aggregate demand forecasts for camping trailers during each of the next three periods (six months) are: Period ; 869

Period 2; 1,730

Period 3; 1,374 MT employs 40 permanent workers. The employees are paid an average of $20 per hour (including fringe benefits) and work approximately 320 hours a period (2 months). The 40 permanent workers can 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 $2,000 and layoff cost is $1,000 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 forecast demand, but shortage during a period (except last) may be possible, in which case the shortage is backordered at the cost of $600 per camping trailer per period backordered. (LO2) a) Calculate all the relevant unit costs. b) Suppose MT uses permanent workers during regular time and overtime. Determine the minimum cost aggregate production plan in this case. c) Suppose MT hires temporary workers, but decides not to use permanent workers during overtime (just regular time). Determine the minimum cost aggregate production plan in this case. Note: Use multiples of 25 units of production per period (i.e., the production of one temporary worker per period). d) Would overtime production by permanent workers and regular time production by temporary workers simultaneously result in a lower total cost? Do a trade-off analysis. What is the overall minimum cost aggregate production plan?