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.

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)

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b) The derivative is ...

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

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

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

r' (10) = 990