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11 June, 20:45

Widget Wonders produces widgets. They

have found that the cost, o (x), of making x

widgets is a quadratic function in terms of x.

The company also discovered that it costs

$20.50 to produce 3 widgets. $60.50 to

produce 7 widgets, and $133 to produce 12

widgets.

What is the total cost of producing nine widgets

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Answers (1)
  1. 11 June, 20:53
    0
    Find the total cost of producing 5 widgets. Widget Wonders produces widgets. They have found that the cost, c (x), of making x widgets is a quadratic function in terms of x. The company also discovered that it costs $15.50 to produce 3 widgets, $23.50 to produce 7 widgets, and $56 to produce 12 widgets.

    OK ... so we have

    a (7) ^2 + b (7) + c = 23.50 → 49a + 7b + c = 23.50 (1)

    a (3) ^2 + b (3) + c = 15.50 → 9a + 3b + c = 15.50 subtracting the second equation from the first, we have

    40a + 4b = 8 → 10a + b = 2 (2)

    Also

    a (12) ^2 + b (12) + c = 56 → 144a + 12b + c = 56 and subtracting (1) from this gives us

    95a + 5b = 32.50

    And using (2) we have

    95a + 5b = 32.50 (3)

    10a + b = 2.00 multiplying the second equation by - 5 and adding this to (3), we have

    45a = 22.50 divide both sides by 45 and a = 1/2 and using (2) to find b, we have

    10 (1/2) + b = 2

    5 + b = 2 b = - 3

    And we can use 9a + 3b + c = 15.50 to find "c"

    9 (1/2) + 3 (-3) + c = 15.50

    9/2 - 9 + c = 15.50

    -4.5 + c = 15.50

    c = 20

    So our function is

    c (x) = (1/2) x^2 - (3) x + 20

    And the cost to produce 5 widgets is = $17.50
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