Please answer the following questions independently:

Develop aggregate production plans and calculate the corresponding relevant costs using the following strategies $($Plan A & B$).$ Assume that hired workers will work from the first day of the hiring month and laid$-$off workers will stop working on the first day of the month. Use the worksheet template posted on eClass.

$($a$)$ Plan A: PMC wants to meet the exact demand for heavy$-$duty tools each month and the planned ending inventory for the $6$th month by varying the workforce $($chase strategy$).$ No overtime, back$-$ordering or subcontracting is allowed.

$($b$)$ Plan B: Use maximum overtime in month $1.$ Layoff three workers at the beginning of the second month and use as much overtime as you need in month two to meet the exact requirements of the second month. Hire one worker at the beginning of the third month, two workers at the beginning of the fourth month and another one at the start of the fifth month. In month four, use maximum overtime first and then, if required, apply subcontracting. While in month five, overtime is not allowed, but you can use the subcontracting option. In the last month, no hiring or layoff is permitted. Only use as much overtime as you need to meet the required units, including the planned ending inventory$-$no excess or shortage of units allowed in the second, fourth and fifth months.

Note: Overtime is allowed only in $1$st$,2$nd$,4$th$,$ and $6$th months; hiring worker$/$s is permitted only in $3$d$,4$th$,$ and $5$th months; and a layoff of worker$/$s is allowed only in the $2$nd month. Subcontracting is permitted $4$th and $5$th months.

$($c$)$ How many workers are required monthly if PMC wants to apply a level strategy? No aggregate production plan or cost details are needed. Just state how many workers are required.