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

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

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Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
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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.

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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.
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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 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

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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. 
Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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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