Problem $11-5($Algo$)$

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 $145$ engines per month. Regular output has a cost of $\backslash (\backslash$$ $60\backslash )$ per engine. The beginning inventory is zero engines. Overtime has a cost of $\backslash (\backslash$$ $110\backslash )$ per engine.

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.

Note: Negative amounts should be indicated by a minus sign. Leave no cells blank $-$ be certain to enter $"0"$ wherever required.

b$.$ Compare the costs to a level plan that uses inventory to absorb fluctuations. Inventory carrying cost is $\backslash (\backslash$$ $2\backslash )$ per engine per month. Backlog cost is $\backslash (\backslash$$ $125\backslash )$ 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.

Note: 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.