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Suppose that the manufacturer of a gas clothes dryer has found​ that, when the unit price is p​ dollars, the revenue R​ (in dollars) is R(p) = -6p²+24,000p.
What unit price should be established for the dryer to maximize​ revenue? What is the maximum​ revenue?

Respuesta :

Answer:

Unit price at maximum revenue is $2,000

maximum revenue is $24,000,000

Step-by-step explanation:

in this question, we are trying to calculate the unit price for the dryer to maximize revenue and the maximum revenue it self.

Now to find the unit price for the maximum revenue, we find the first derivative and set to zero, since at turning points, first derivative = 0

This means that;

dR(p)/dp = -12p + 24,000 = 0

12p = 24,000

p = 24,000/12

p = $2,000

To find the maximum revenue at this price, we simply input this value into the equation

R(2000) = -6(2,000)^2 + 24,000(2,000)

-24,000,000 + 48,000,000 = $24,000,000

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