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.

$\backslash$table$[[,$Month$],[,1,2,3,4,5,6,7,8,$Total,$],[$Forecast$,120,135,140,120,125,125,132,135,1,032,]]$

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.$)$

Answer is not complete.

$\backslash$table$[[$Period$,1,2,3,4,5,6,7],[$Forecast$,120,135,,,,,],[$Output$,,,,,,,],[$Regular$,135x,135vv,135vv,135x,135x,135x,135x$