help 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.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline & $\backslash$multicolumn$\{9\}\{|$c$|\}\{$Month$\}\backslash \backslash$

$\backslash$hline & $1$ & $2$ & $3$ & $4$ & $5$ & $6$ & $7$ & $8$ & Total $\backslash \backslash$

$\backslash$hline Forecast & $125$ & $135$ & $143$ & $144$ & $125$ & $165$ & $140$ & $143$ & $1,120\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

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: Negatlve amounts should be Indlcated by a minus sign. Leave no cells blank $-$ be certaln to enter $"0"$ wherever required.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline Period & $1$ & $2$ & $3$ & $4$ & $5$ & $6$ & $7$ & $8$ & Total $\backslash \backslash$

$\backslash$hline Forecast & $125$ & $135$ & $143$ & $144$ & $125$ & $165$ & $140$ & $143$ & $1,120\backslash \backslash$

$\backslash$hline Output & & & & & & & & & $\backslash \backslash$

$\backslash$hline Regular & & & & & & & & & $\backslash \backslash$

$\backslash$hline Overtime & & & & & & & & & $\backslash \backslash$

$\backslash$hline Output $-$ Forecast & & & & & & & & & $\backslash \backslash$

$\backslash$hline Costs & & & & & & & & & $\backslash \backslash$

$\backslash$hline Output & & & & & & & & & $\backslash \backslash$

$\backslash$hline Regular & & & & & & & & & $\backslash \backslash$

$\backslash$hline Overtime & & & & & & & & & $\backslash \backslash$

$\backslash$hline Total & & & & & & & & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$ 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 $"$O$"$ wherever required. Round average Inventory row, Inventory cost row, and Total row values to $1$ decimal.