Question

Suppose that the demand and price for honeydew melons are related by the equation q = 5900 – 800 p , where q is in thousands and p is in dollars. What price will give the maximum revenue? What is the maximum revenue?

Answer 1

revenue = demand * price

              = q * p

              = (5900 - 800 * p) * p

              = 5900 p - 800 p²

To maximize revenue we need to equate the derivative of this function to zero

d(revenue) / dp = 0

or, d/dp (5900p - 800p²) = 0

or, 5900 - 2 * 800 * p = 0

or, p = 3.6875

Maximum revenue = 5900 * 3.6875 - 800 * 3.6875² = 10878.125