A manufactureer determines that the number of drills it can sell is given by the formula D= -3p^2 + 174p - 310 where p is the price of the drills in dollars
at what price will the manufacturer sell the maximum number of drills?
Tutors, please sign in to answer this question.
D= -3p2 + 174p - 310
Let's take the derivative and set it equal to zero.
The answer is $29.
This is the vertex of the downward parabola. We know it is downward because 3p2 is negative. The vertex is the point at which rate of change is zero.
What is the question?
How many should be sold to have maximum profit.
D(p) = -3p^2 + 174 p- 310
D Maximum ( p) = -b/2a = -174/ -6 = 29
D( 19) = -3(19^2) +174*19 -310=
This is a parabola, which opens down. Therefore, at its vertex you get the maximum number of drills.
P = -b/(2a) = -174/(2(-3)) = $29 <==Answer