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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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sqdancefan

Answer:

  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