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:

Period $1$ Period $2$ Period $3$

$8691,7301,374$

MT employs $40$ permanent workers who are paid an average of $$20$ per hour $($including fringe benefits$)$ and work approximately $320$ hours a period $(2$ months$).$ They make a p proximately $1,000$ camping trailers per period during regular time. They can also work up to $50$ percent more as overtime $($i$.$e$.,$ up to $12$ hours a day vs$.$ the regular $8$ hours a day$)$ and will be paid $1\mathrm{.}5$ times the regular wage rate. Alternatively, MT can hire up to $40$ additional temporary workers to work during a second shift. Hiring cost is $$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 $($a l though 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. $($Round the Production time per unit answer to $2$ decimal places.$)$

Production per worker per period

Production time per unit

hrs

Labour cost per unit $($regular time$)$ $

Labour cost per unit $($over time$)$ $

Hiring cost per unit $

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.

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 plan in this case. Hint: Hire $15$ temps for two periods and $9$ temps for $1$ period starting in period $2.$

The minimum cost aggregate production plan in the above case $

d$-1.$ What is the overall minimum cost plan?

The overall minimum cost aggregate production plan $

d$-2.$ Would overtime production by permanent workers and regular time production by temporary workers simultaneously result in a lower total cost?

multiple choice

Yes

No