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26 April, 12:41

A company manufacturers and sells x electric drills per month. The monthly cost and price-demand equations are

C (x) = 64000+60x, p=190-x/30, 0≤x≤5000.

a) production level at max revenue = 2850

b) price to max profit = $125

c) Suppose that a 5 dollar per drill tax is imposed. Determine the number of drills that should be produced and sold in order to maximize profit under these new circumstances.?

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  1. 26 April, 12:53
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    A.

    Revenue x * p = 220x - x^2/30

    d/dx = 220 * 15 = 3300

    B.

    Profit = Revenue - Cost

    = 220x - x^2/30 - 72000 - 80x

    d/dx = 220 - x/15 - 80 = 0

    x = 15 * 140 = 2100

    p = 220 - 2100/30 = 220 - 70 = $150

    C.

    With $5 tax the price-demand equation should be

    p = 220 - x/30 + 5

    Profit = 225x - x^2/30 - 72000 - 80x

    d/dx = 225 - x/15 - 80 = 0

    x = 15 * 145 = 2175
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