Manager T$.$ C$.$ Downs of Plum Engines, a producer of lawn mowers and leaf blowers, must develop an aggregate plan giv forecast for engine demand shown in the table. The department has a regular output capacity of $145$ engines per month. output has a cost of $$60$ per engine. The beginning inventory is zero engines. Overtime has a cost of $$110$ per engine.

$\backslash$table$[[,$Month$],[,,,,,,,,,,],[,1,2,3,4,5,6,7,8,$Total,$]]$