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Math Help - Multiple choice price and quantity

  1. #1
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    Multiple choice price and quantity

    Maths multiple choice question?

    Each week, a company can sell x units of its product at a price of p dollars each,
    where p = 250 - 4x. The total cost of producing x units is 4800 - 70x. Note that
    revenue is equal to price times quantity. What quantity or quantities should the
    company produce if it aims to break even?
    (a) 20 units;
    (b) 60 units;
    (c) 20 or 60 units;
    (d) 40 units.
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  2. #2
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    Hello marie7
    Quote Originally Posted by marie7 View Post
    Maths multiple choice question?

    Each week, a company can sell x units of its product at a price of p dollars each,
    where p = 250 - 4x. The total cost of producing x units is 4800 - 70x. Note that
    revenue is equal to price times quantity. What quantity or quantities should the
    company produce if it aims to break even?
    (a) 20 units;
    (b) 60 units;
    (c) 20 or 60 units;
    (d) 40 units.
    The company sells x units at (250-4x) dollars each. The revenue from this is x \times (250-4x). If they break even, then this revenue is equal to the total production cost, which is (4800-70x) dollars. So:

    x(250-4x)=4800-70x

    \Rightarrow 250x-4x^2 = 4800-70x

    \Rightarrow 4x^2 -320x+4800=0

    \Rightarrow x^2-80x+1200=0

    \Rightarrow(x-20)(x-60)=0

    \Rightarrow x = 20 or x=60

    So the answer is (c).

    Grandad
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