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13 June, 20:11

The number N of cars produced at a certain factory in 1 day after t hours of operation is given by Upper N (t) equals 800 t minus 5 t squared commaN (t) = 800t-5t2, 0 less than or equals t less than or equals 10.0≤t≤10. If the cost C (in dollars) of producing N cars is Upper C (Upper N) equals 30 comma 000 plus 8000 Upper N commaC (N) = 30,000+8000N, find the cost C as a function of the time of operation of the factory. What is the cost C as a function of the time t of operation of the factory?

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  1. 13 June, 20:34
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    The cost C as a function of t is C (t) = 30,000 + 6,400,000 t - 40,000 t²

    Step-by-step explanation:

    The function N (t) = 800 t - 5t², represents the number of cars produced at a time t hours in a day, where 0 ≤ t ≤ 10

    The function C (N) = 30,000 + 8,000 N, represents the cost C (in dollars) of producing N cars

    We need to find The cost C as a function of the time t

    That means Substitute N in C by its function by other word find the composite function (C о N) (t)

    ∵ C (N) = 30,000 + 8,000 N

    ∵ N (t) = 800 t - 5 t²

    - Substitute N in C by 800 t - 5 t²

    ∴ C (N (t)) = 30,000 + 8000 (800 t - 5 t²)

    - Multiply the bracket by 8000

    ∴ C (N (t)) = 30,000 + 8000 (800 t) - 8000 (5 t²)

    ∴ C (N (t)) = 30,000 + 6,400,000 t - 40,000 t²

    - C (N (t) = C (t)

    ∴ C (t) = 30,000 + 6,400,000 t - 40,000 t²

    The cost C as a function of t is C (t) = 30,000 + 6,400,000 t - 40,000 t²
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