A small publishing company is releasing a new book. The production costs will include a one-time fixed cost for editing and an additional cost for each book printed. The total production cost (in dollars) is given by the function , where is the number of books. The total revenue earned (in dollars) from selling the books is given by the function . Let be the profit made (in dollars). Write an equation relating to . Simplify your answer as much as possible.

Profit Function =  P.Q - [A + C (Q)]

Explanation:

Profit = Total Revenue - Total Cost

Let Q be the quantity

Total Revenue = Price x Quantity = P X Q

Total Cost =  Total Fixed Cost + Total Variable Cost

= A + C (Q) ;

where A = Autonomous fixed cost, irrespective of level of output , C (Q) is functional form of variable cost in terms of Quantity of production

Profit = P.Q - [A + C (Q)]  

Letting : P = 10, C = 2Q , Q = 3 , A = 2

Profit would be : P.Q - [A + C (Q)]  

= (10)X(3) - [ 2 + 2(3)]

= 30 - (2 + 6) =  30 - 8

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