A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars a

Question

A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the unit cost is given by the function C(x) = 0.9x^2 -234x + 23,194 . How many cars must be made to minimize the unit cost?
Do not round your answer.

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Sophia 3 days 2021-09-15T18:42:48+00:00 1 Answer 0

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    2021-09-15T18:43:58+00:00

    Answer:

    130 cars.

    Step-by-step explanation:

    The cost function is given by:

    C(x) = 0.9x^2 -234x + 23,194; where x is the input and C is the total cost of production.

    To find the minimum the unit cost, there must be a certain number of cars which have to be produced. To find that, take the first derivative of C(x) with respect to x:

    C'(x) = 2(0.9x) – 234 = 1.8x – 234.

    To minimize the cost, put C'(x) = 0. Therefore:

    1.8x – 234 = 0.

    Solving for x gives:

    1.8x = 234.

    x = 234/1.8.

    x = 130 units of cars.

    To check whether the number of cars are minimum, the second derivative of C(x) with respect to x:

    C”(x) = 1.8. Since 1.8 > 0, this shows that x = 130 is the minimum value.

    Therefore, the cars to be made to minimize the unit cost = 130 cars!!!

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