Question 675543: Chocolate Confections, Inc. has determined that when x chocolate cakes are made daily, the average cost per chocolate cake is given by C(x)=0.001x^2-0.14x+12.20
a) What is the average cost per cake if 30 chocolate cakes are made daily?
b) How many chocolate cakes should be made daily in order to minimize the average cost per cake? Show work
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Chocolate Confections, Inc. has determined that when x chocolate cakes are made daily, the average cost per chocolate cake is given by C(x)=0.001x^2-0.14x+12.20
a) What is the average cost per cake if 30 chocolate cakes are made daily?
set x to 30 and solve for C(x):
C(x)=0.001x^2-0.14x+12.20
C(30)=0.001(30)^2-0.14(30)+12.20
C(30)=0.9-4.2+12.20
C(30)=-3.3+12.20
C(30)=$8.90
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b) How many chocolate cakes should be made daily in order to minimize the average cost per cake? Show work
The given equation:
C(x)=0.001x^2-0.14x+12.20
is a parabola that opens upwards, therefore the vertex is the minimum:
x = -b/(2a)
x = -(-0.14)/(2*0.001)
x = 0.14/(0.002)
x = 70 cakes
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