Problema Solution
A manufacturer determines that the number of drills it can sell is given by the formula D=-3p^2+180p-285, where p is the price of the drills in dollars. At what price will the manufacturer sell the maximum number of drills? What is the maximum number of drills that can be sold?
Answer provided by our tutors
Given this,
To find where the maximum is, find where the derivative is equal to zero. So first find the derivative.
D = -3p^2 + 180p - 285
D' = -6p + 180
-6p + 180 = 0
p = 30
So the manufacturer will sell the maximum number of drills when the price is $30.
just find D when p is 30:
D = -3p^2 + 180p - 285
D = -3*30^2 + 180*30 - 285
D = 2415
So the maximum number of drills that can be sold is 2,415.