math

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can someone show me how to solve this problem.

It determines that in order to sell x smartphones, the price per product must be p=280-0.4x. It also determine that the total cost of producing x smartphones is given by C(x)=5000+0.6x.
a. Find the total revenue, R(x).
b. Find the total profit, P(x).
c. How many smartphones must the company sell in order to maximize profit?
d. What is the maximum profit?
e. What is th price per smartphone must be charged in order to maximize profit?

can u please show me the steps to solve this and the final ans. x need to calculate.

  • math -

    R(x) = p(x)*x
    P(x) = R(x)-C(x)
    P(x) = x(280-.4x) - (5000+.6x)
    = -.4x^2 + 279.4x - 5000

    This is a parabola, with maximum at x = -279.4/-.8 = 349.25

    plug that x into the functions to get profit and price.

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