Help with a math problem! Finding break even points.?

A sporting goods store finds that if it sells x exercise machines per day, then its costs will be

C(x) = 80x + 8000

and its revenue will be

R(x) = −2x2 + 360x

(both in dollars).

(a) Find the store s break-even points.

(b) Find the number of sales that will maximize profit, and find the maximum profit.

2 Answers

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  • TomV
    Lv 7
    6 months ago

    a) Break even point is where cost and revenue are equal.

    C(x) = R(x)

    80x + 8000 = -2x² + 360x

    2x² - 280x + 8000 = 0

    x² - 140x + 4000 = 0

    (x-40)(x-100) = 0

    x = 40, 100

    Break even points are sales of 40 or 100 machines per day.

    b) Profit is Revenue minus cost.

    P(x) = R(x) - C(x)

    P(x) = -2x² + 360x - 80x - 8000

    = -2x² + 280x - 8000

    dP/dx = - 4x + 280 = 0

    x = 70

    P(70) = -2(70)² + 280(70) - 8000 = 1800

    Maximum profit of $1800 per day occurs at 70 sales per day.

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  • Anonymous
    6 months ago

    start by graphing both functions

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