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8 December, 02:09

The total cost of producing a type of car is given by C (x) = 12000-40x+0.04x2, where x is the number of cars produced. How many cars should be produced to incur minimum cost?

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  1. 8 December, 02:30
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    Step-by-step explanation:

    C' (x) = -40+0.08 x

    C' (x) = 0 gives

    -40+0.08 x=0

    x=40/0.08=500

    C" (x) = 0.08>0 at x=500

    so C (x) is minimum if x=500

    so 500 cars need to be produced for minimum cost.

    or we can solve by completing the squares.

    c (x) = 12000+0.04 (x²-1000 x+250000-250000)

    =12000+0.04 (x-500) ²-0.04*250000

    =0.04 (x-500) ²+12000-10000

    =0.04 (x-500) ²+2000

    c (x) is minimum if x=500
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