Question

A manufacturer determines that the number of drills it can sell is given by the formula D(p) = -4p^2 + 160p - 3.

At what price will the manufacturer sell the maximum number of drills in dollars ($)?""

This question relates to finding the price at which the manufacturer will sell the maximum number of drills using the given formula.

Answer 1

The maximum number of drills will be sold at a price of $40.

Step-by-step explanation:

To find the price at which the manufacturer will sell the maximum number of drills, we need to determine the vertex of the quadratic function D(p) = -4p^2 + 160p - 3. The vertex of a quadratic function in the form ax^2 + bx + c is given by the formula x = -b/2a. In this case, a = -4 and b = 160.

Plugging these values into the formula, we get p = -160/(2*-4) = 40. Therefore, the price at which the manufacturer will sell the maximum number of drills is $40.