Inequalities and Problem Solving

16. Revenue and Cost Functions A company produces and sells x units of a product. Revenue Function R(x) = (price per unit sold)x Cost Function C(x) = fixed cost + (cost per unit produced)x

17. The Profit Function The profit, P(x), generated after producing and selling x units of a product is given by the profit function P(x) = R(x) � C(x) where R and C are the revenue and cost functions, respectively.

18. Business Application EXAMPLE A company that manufactures motorbikes has a fixed cost of $14,000. It costs $1900 to produce each motorbike. The selling price per motorbike is $2400. Write the cost function, the revenue function and the profit function. Determine how many bikes must be produced and sold to have a profit. Cost Function: C(x) = 14,000 + 1900x

19. Business Application Revenue Function: R(x) = 2400x Profit Function: P(x) = R(x) � C(x) = 2400x � (14,000 + 1900x) = 2400x � 14,000 - 1900x = 500x � 14,000

20. Business Application How many must be sold to make a profit? P(x) = 500x � 14,000 A profit occurs when P(x) > 0 500x � 14,000 > 0 500x > 14,000 x > 28 More than 28 motorbikes must be produced and sold to make a profit.