A manufacturer of industrial seafood processing equipment $($scaler$)$ wants you to develop an aggregate plan for the six quarters of the upcoming year and a half using the following data on demand and capacity, along with cost numbers$/$per unit. Demand for $6$ quarters are as follows $$

Q$1$: $400,$ Q$2$: $850,$ Q$3$: $1,000,$ Q$4$: $450,$ Q$5$: $925,$ Q$6$: $1,100.$ Previous quarter's output was $500$ units.

Initial inventory is $250$ units.

Overtime capacity for the planning period is $200$ units$/$quarter$.$

The manufacture's subcontractor can supply $1000$ units$/$quarter$,$ if needed.

Regular time cost is $$7\mathrm{.}50/$unit$.$ Overtime costs $$4\mathrm{.}00$ extra$/$unit$.$ The subcontracting cost is $$13\mathrm{.}75/$unit$.$ Carrying cost is $$5\mathrm{.}75/$unit$/$quarter$.$ To increase staffing it's $$35/$unit$,$ and $$50/$unit to decrease staffing. Stock$-$out cost is $$8\mathrm{.}55$ per unit. No back$-$ordering is allowed.

a$.$ Produce utilizing a strategy that varies the workforce based on the prior quarter. This will be Plan A$.$ What is the cost of the plan?

$[$ Select $]$

$.$ Were any sales lost during the planning period?

$[$ Select $]$

Note: Do not use the inventory right away; plan to just chase the prior quarter's demand.

b$.$ Produce utilizing a level strategy by producing at a rate of the $570$ for the planning period. This will be Plan B$.$ What is the cost of the plan?

$[$ Select $]$

Was there a need to carry over inventory throughout the planning period?

$[$ Select $]$

c$.$ Produce utilizing a mixed strategy producing $350$ units per quarter, then utilizing overtime and subcontracting, if needed. This will be Plan C$.$ What is the cost of this plan?

$[$ Select $]$

d$.$ Based on cost$,$ which plan should be selected?

$[$ Select $]$