Given the projected demands for the next six months, prepare an aggregate plan that uses inventory, regular time, overtime, subcontract and backorders. Regular time is limited to $150$ units per month $($Cost per Unit $=$ $$50).$ Overtime is limited to a maximum of $20$ units per month $($Cost per Unit $=$$$75).$ Units purchased from the subcontractor $($Cost per Unit $=$ $$63)$ cannot exceed $50$ per month and the total purchases from the subcontractor over the $6$ month period cannot be over $100$ units. Backorders cannot exceed $40$ units in any given month $($Cost per Unit $=$ $$2)$ and must be no more than $30$ in Period $6.$ Average Inventory Holding cost per Unit $=$ $$5.$ Forecasted Demand as well as Beginning and desired Ending Inventory are listed in the table below.

Total Cost Month $1=$

Hint: Range $(8220,8310)$

Total Cost Month $2=$

Hint: Range $(10930,10960)$

Total Cost Month $3=$

Total Cost Month $4=$

Total Cost Month $5=$

Hint: Range $(8190,8280)$

Total Cost Month $6=$

Total Cost All Periods $=$

Hint: Range $(58265,58465)\backslash$table$[[$Month$,1,2,3,4,5,6,$Total$],[$Regular Output$],[$Overtime Output$],[$Subcontract$],[$Beginning Inventory,$20,,,,,,],[$Total Available for Sale$],[$Less Forecast,$180,180,280,150,160,180,],[$Plus Backlog$-$Current Period$],[\backslash$table$[[$Less Backlog$-$Previous$],[$Period$]]],[$Ending Inventory,,,,,,$10,],[$Average Inventory,,,,,,,$]]$