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 $$ Q$1400,$ Q$2850,$ Q$31,000,$ Q$4450,$ Q$5925,$ Q$61,100.$ Overtime capacity for the planning period is $200$ units$/$quarter$.$ The manufacture's subcontractor can supply $250$ units$/$quarter$,$ if needed. Initial inventory is $250$ units. Regular time cost is $$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 $$5$