Decorum Incorporated manufactures high$-$end ceiling fans. Their sales are seasonal with higher demand in the warmer summer months. Typically, sales average $400$ units per month. However, in the hot summer months $($June$,$ July, and August$),$ sales spike up to $600$ units per month. Decorum can produce up to $500$ units per month at a cost of $$305$ each. By bringing in temporary workers, Decorum can produce up to an additional $75$ units at a cost of $$345$ each. Decorum sells the ceiling fans for $$510$ each. Decorum can carry inventory from one month to the next, but at a cost of $$15$ per ceiling fan per month. Decorum has $15$ units in inventory at the start of January.

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Build and solve a linear programming spreadsheet model to maximize the profit over all $12$ months.

Assuming Decorum must produce enough ceiling fans to meet demand, how many ceiling fans should Decorum produce each month $($using their regular labor force and$/$or temporary workers$)$ over the course of the next year so as to maximize their total profit?

Determine the net profit.