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 $136$ engines per month. Regular output has a cost of $\backslash (\backslash$$ $50\backslash )$ per engine. The beginning inventory is zero engines. Overtime has a cost of $\backslash (\backslash$$ $110\backslash )$ per engine.

$\backslash$begin$\{$tabular$\}\{$cccccccccc$\}$

& $\backslash$multicolumn$\{1\}\{$c$\}\{$ Month $\}\backslash \backslash$

$\backslash$cline $\{2-11\}$ Forecast & $1$ & $2$ & $3$ & $4$ & $5$ & $6$ & $7$ & $8$ & Total $\backslash \backslash$

& $96$ & $135$ & $143$ & $165$ & $125$ & $125$ & $140$ & $143$ & $1,072$

$\backslash$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: Negative amounts should be indicated by a minus sign. Leave no cells blank $-$ be certain 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 & $96$ & $135$ & $143$ & $165$ & $125$ & $125$ & $140$ & $143$ & $1,072\backslash \backslash$

$\backslash$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$\}$