SOLUTION: A company has determined that when x hundred dulcimers are​ built, the average cost per dulcimer can be estimated by ​C(x)=0.2xsquared−2.6x+9.950​, where&#8

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Question 1114779: A company has determined that when x hundred dulcimers are​ built, the average cost per dulcimer can be estimated by ​C(x)=0.2xsquared−2.6x+9.950​, where​ C(x) is in hundreds of dollars. What is the minimum average cost per dulcimer and how many dulcimers should be built to achieve that​ minimum?
The minimum average cost per dulcimer is ​$______. Thank you in advance!
Found 2 solutions by Boreal, Fombitz:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
c(x)=0.2x^2-2.6x+9.950
vertex is minimum and occurs at x=-b/2a
x=2.6/0.4=6.5
This is 650 altogether, since x is hundreds
c(6.5)=0.2*43.25-2.6(6.5)+9.950=1.7 or $1.70.
graph%28300%2C300%2C-5%2C20%2C-10%2C50%2C0.2x%5E2-2.6x%2B9.950%29

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
C%28x%29=0.2x%5E2-2.6x%2B9.950
Convert to the vertex form,
C%28x%29=0.2%28x%5E2-13x%29%2B9.950
C%28x%29=0.2%28x%5E2-13x%2B%2813%2F2%29%5E2%29%2B9.950-0.2%2813%2F2%29%5E2
C%28x%29=0.2%28x-13%2F2%29%5E2-1.5
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.
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The minimum occurs at the vertex.
So (13%2F2, 1.5)
Multiply both values by 100.
So building 650 dulcimers, would give you a min cost of $150.