The cost C 15 Suppose that the revenue R in dollars from sel

The cost C 15. Suppose that the revenue R, in dollars, from selling x cell phones, in hundreds, is R(x)14x 164x. The cost C. in dollars, from selling × cell phones, in hundreds, is co-o 06x3-2x2 + 35x + 750. (a) Find the profit function, P(x)= R(x)-C(x) (b) Find the profit if x= 25 hundred cell phones are sold. (c) Interpret P(25). (a) P(x)= (Use integers or decimals for any numbers in the expression.) (b) P(25) S (Type an integer or a decimal. Round to the nearest cent) (c) Interpret P(25). Choose the correct answer below A. When 25 hundred cel phones are sold, the revenue is given by P/25) B. When 25 hundred cell phones are sold, the profit is given by P(25) C. When 25 hundred cell phones are sold, the cost is given by P(25)

Solution

R(x) = -1.4x^2 + 164x

C(x) = 0.06x^3 – 2x^2 + 35x + 750

(a) P(x) = R(x) – C(x) = (-1.4x^2 + 164x) – (0.06x^3 – 2x^2 + 35x + 750)

                                    = 0.06x^3 + 0.6x^2 + 129x – 750

(b) P(25) = 0.06*25^3 + 0.6*25^2 + 129*25 – 750 = 3787.5 dollars

(c) Option B) is correct