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?

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# 3 Answers

Hi Robert;

D= -3p

^{2}+ 174p - 310Let's take the derivative and set it equal to zero.

0=-6p+174

-174=-6p

29=p

The answer is $29.

This is the vertex of the downward parabola. We know it is downward because 3p

^{2}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=

1913

# Comments

this was the next question but I assumed I needed to solve for p first which is $29. been a long time since I have used parabola. my daughter was studying for her final and had not covered this in class this semester.

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

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