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at what price will the manufacturer sell the maximum number of drills?

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3 Answers

Hi Robert;
D= -3p2 + 174p - 310
Let'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 3p2 is negative.  The vertex is the point at which rate of change is zero.

Comments

Thanks Vivian My daughter asked me tonight this question and I could not remember how to solve it. Been a long time since I used parabola. She has not covered this in class yet and I could not find it in her book but it is on her midterm final in algebra 2.

Comment

 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. 

Comment

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