Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

The profit function for a new product is given by y= -4x^2 + 28x - 40, where x is the number sold in thousands. How many to break even?

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  • 2 months ago
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    The break even point is where the profit is 0.

    Set it to zero and solve for x:

    -4x² + 28x - 40 = 0

    Let's simplify that by dividing everything by -4:

    x² - 7x + 10 = 0

    Factor that:(x - 2)(x - 5) = 0

    So there are two potential solutions:

    x = 2 or x = 5

    Anything before 2 (thousand) units, they are losing money.

    They break even when they sell 2 (thousand) units.

    After that, the profit is positive.

    When they sell 5 (thousand) units, they again are back to a profit of 0.

    Anything above 5 (thousand) units, they are losing money once more.

    Answer:

    2 (thousand) or 5 (thousand) to break even.

  • y = 0

    0 = -4x^2 + 28x - 40

    0 = x^2 - 7x + 10

    x = (7 +/- sqrt(49 - 40)) / 2

    x = (7 +/- sqrt(9)) / 2

    x = (7 +/- 3) / 2

    x = 4/2 , 10/2

    x = 2 , 5

    After 2000 sold, they break even.  Their profit peaks at 3500 sold and they start to lose money after 5000 sold.

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