Question

A company that manufactures flash drives knows that the number of drives x it can sell each week is related to the price

Answer 1

Answer:

• $7.50
• $5625

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.