Question $7$

A large Billings, MT feed mill Longhorn Processing, prepares its $6-$month aggregate plan by forecasting demand for $50-$LB bags of cattle feed as follows:

Previous quarter's output was $900$ bags.

The feed mill plans to begin the new year with $100$ bags of beginning inventory left over from the previous month.

Overtime capacity is set at $300$ bags per month.

A friendly competitor in Grand Forks, ND is also available as a backup source $($subcontractor$)$ to meet demand during the $6-$month period.

Cost on regular time per bag is $$13\mathrm{.}25$; Overtime cost is $$6\mathrm{.}25$ extra; subcontracting cost $$22\mathrm{.}50.$ Carrying cost is $3\mathrm{.}50$ per bag.

If Longhorn decides to hire or layoff, the costs would be $$27\mathrm{.}00$&$$41\mathrm{.}00$ per bag respectively.

a$.$ Utilizing a Chase strategy $($vary the workforce$),$ based on the current period, what is the total cost of the plan?

b$.$ Utilizing a level strategy with a constant production rate of $1,400$ units, then utilizing overtime and subcontract, if needed $($refer to the capacity limits$).$ What is the cost of this plan:

Were any units subcontracted, and how many?

c$.$ Utilize a level strategy at the minimum period demand forecast over the $6-$month period, then utilize the subcontractor, if needed $($no overtime$).$ What is the cost of this plan?