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2 April, 05:44

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A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function C (x) = 0.5x^2-150 + 21,035. How many machines must be made to minimize the unit cost?

Do not round your answer.

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  1. 2 April, 08:00
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    1 machine must be made to minimise the unit cost.

    Step-by-step explanation:

    Step 1: Identify the function

    x is the number of machines

    C (x) is the function for unit cost

    C (x) = 0.5x^2-150 + 21,035

    Step 2: Substitute values in x to find the unit cost

    C (x) = 0.5x^2-150 + 21,035

    The lowest value of x could be 1

    To check the lowest cost, substitute x=1 and x=2 in the equation.

    When x=1

    C (x) = 0.5x^2-150 + 21,035

    C (x) = 0.5 (1) ^2-150 + 21,035

    C (x) = 20885.5

    When x=2

    C (x) = 0.5x^2-150 + 21,035

    C (x) = 0.5 (2) ^2-150 + 21,035

    C (x) = 20887

    We can see that when the value of x i. e. the number of machines increases, per unit cost increases.

    Therefore, 1 machine must be made to minimise the unit cost.

    !
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