19. The owner of a leather craft shop has determined that he can sell x attaché cases if the price is p = D(x)= 46+0.25x dollars. The total cost for these cases is C(x)=0.15x² +6x +190 dollars. a. Find the revenue function R(x). b. Find the profit function P(x). Find P(25), P(30), and P(40). d. Find the marginal profit function P'(x). e. Find P'(25), P'(30), and P'(40). c.

4. It costs C(x) = 112 + 1.4x dollars to produce x Specialty Hair Ribbons. To sell x Specialty Hair Ribbons, the price should be set at p(x) = 18 - 0.2x. a.Find the revenue function R(x) and the profit function P(x) when the manufacturer makes and sells x ribbons. Simplify your functions. R(x) P(x) b. How many ribbons should be made and sold to break even? Round your answers) to the nearest whole number and include units. What profit (or loss) does the manufacture incur when they make and sell 32 ribbons? Circle profit or loss and fill in the blank below rounding to the nearest whole dollar. At a production level of 32 Ribbons, they have a profit / 1OSS of

Suppose that the total revenue from producing and selling q items is given by R(q) = 50g – 0.5q? - and the total cost of producing q items is given by C(q) = 4q + 10 (a) What is the profit function P(q)? (b) What is the maximum profit? (c) How many items must be produced and sold to yield the maximum profit?

A Midwestern factory has been studying their costs and estimates the total cost for an upcoming production run can be modeled by C(x) = 41000 + 80x + x³ dollars. The total revenue from the sale of x units is R(x) = 3680x dollars. Before they start production, they want to know if it will be worthwhile... That is, can they make money? (a) Find the profit function, (b) determine the level of production that will maximize profit, and (c) find the maximum profit possible according to this model. a) The profit function is P(x) = Round the production level to the nearest whole unit. b) The production level per week that results in the maximum profit is Use the whole number you entered above to compute the maximum profit. c) The maximum profit is $