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 $135$ engines per month. Regular output has a cost of $$64$ per engine. The beginning inventory is zero engines. Overtime has a cost of $$114$ per engine.

Month

$12345678$ Total

Forecast $1201351401201251251321351,032$

b$.$ Compare the costs to a level plan that uses inventory to absorb fluctuations. Inventory carrying cost is $$4$ per engine per month. Backlog cost is $$144$ per engine per month. There should not be a backlog in the last month. Set regular production equal to the monthly average of total forecasted demand. Assume that using overtime is not an option. $($Negative amounts should be indicated by a minus sign. Leave no cells blank $-$ be certain to enter $"0"$ wherever required. Round average inventory row, Inventory cost row, and Total row values to $1$ decimal.$)$