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19 August, 05:06

The price in dollars of a stereo system is given by p (q) = (1000/q2) + 1000 where q represents the demand of the product.

a) Find the revenue function.

b) Find the marginal revenue function (derivative).

c) Find the marginal revenue when the demand is 10.

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  1. 19 August, 08:25
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    a) r (q) = 1000 (q + 1/q)

    b) r' (q) = 1000 (1 - 1/q^2)

    c) r' (10) = 990

    Step-by-step explanation:

    a) Revenue is the product of quantity and price:

    r (q) = q·p (q) = q (1000 (1 + 1/q^2))

    r (q) = 1000 (q + 1/q)

    __

    b) The derivative is ...

    r' (q) = 1000 (1 - 1/q^2)

    __

    c) The derivative evaluated for q=10 is ...

    r' (10) = 1000 (1 - 1/10^2) = 1000 (0.99)

    r' (10) = 990
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