A company that manufactures flash drives knows that the number of drives x it can sell each week is related to the price
p, in dollars, of each drive by the equation x=1500−100p. a. Find the price p that will bring in the maximum revenue. Remember, revenue (R) is the product of price (p) and items sold (x), in other words, R=xp.
The price $
will yield the max revenue. b. Find the maximum revenue.
The max revenue is $

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Step-by-step explanation:

Use the given equation, and use your understanding of quadratic functions to reason about the solution.

  R = xp

  R = (1500 -100p)p . . . . . substitute the given expression for x

This is q quadratic function in p. It has zeros where p=0 and p=15. (These are the values that make the factors be zero.) We know this function has a maximum (because we're told to find it, and because p^2 has a negative coefficient). That maximum is the vertex of the parabola, which is located on the line of symmetry, halfway between the zeros.

The maximum revenue is obtained when p = (0+15)/2 = 7.5. That value of revenue is R = (1500 -100·7.5)(7.5) = 5625.

The price $7.50 will yield the maximum revenue, $5625.

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