Manager T$.$ C$.$ Downs of Plum Engines, a producer of lawn mowers and leaf blowers, must develop an aggregate plan given the forecast for engine demand shown in the table. The department has a regular output capacity of $130$ engines per month. Regular output has a cost of $$60$ per engine. The beginning inventory is zero engines. Overtime has a cost of $$90$ per engine.

$\backslash$table$[[,$Month$],[$Forecast$,\backslash$table$[[120]],2,3,4,5,6,7,8,$Total$],[,,135,140,120,125,125,140,135,1,040]]$

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a$.$ Develop a chase plan that matches the forecast and compute the total cost of your plan. Regular production can be less than regular capacity. $($Negative amounts should be indicated by a minus sign. Leave no cells blank $-$ be certain to enter $"$O$"$ wherever required.$)$

$\backslash$table$[[$Period$,1,2,3,4,5,6,7,8,$Total$],[$Forecast$,120,135,140,120,125,125,140,135,1010],[$Output$],[$Regular$,,,,,,,,,],[$Overtime$],[$Subcontract$],[$Output $-$ Forecast$],[$Inventory$],[$Beginning$],[$Ending$],[$Average$],[$Backlog$],[$Costs:$],[$Output$],[$Regular$],[$Overtime$],[$Subcontract$],[$Inventory$],[$Backorder$,,,,,,-,,,]]$