Question $13(1\mathrm{.}5$ points$)$

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Scenario $8\mathrm{.}3-$ Mousetraps

A company faces the aggregate planning problem shown in the table below. Cost of regular production is $$15$ per unit, the cost of producing the same unit on overtime is $$22\mathrm{.}50,$ the cost of subcontracting is $$\mathrm{.}27$ per unit, and the cost of carrying a unit in inventory from one month to the next is $$10.$

$\backslash$table$[[,$July,August,$\backslash$table$[[$Septem$],[$ber$]],$October,$\backslash$table$[[$Novemb$],[$er$]]],[$Forecast$,800,650,450,550,900],[\backslash$table$[[$Beginning$],[$Inventory$]],140,,,,],[$Regular Time,,,,,$],[$Overtime$,,,,,],[$Subcontracting$,,,,,],[$Ending Inventory,,,,,$]]$

The labor contract at the plant prohibits both overtime and subcontracting output to exceed $250$ units in any five$-$month window. The plant capacity is $20$ units per day produced using two shifts and the plant runs seven days a week. By policy, management wants to avoid stockouts.