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?
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
.
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