We have the following given data

C(x)=0.7x2+170x+170x∈[0,500]Cavg=??C(x)=0.7x2+170x+170x∈[0,500]Cavg=??

Solution

The average cost of the first 500 units can be obtained by dividing the total cost of all the units by the number of units:

C(x)=0.7x2+170x+170x∈[0,500]Cavg=Total Cost 500= \int_0^{500} C(x) dx 500=1500∫5000(0.7x2+170x+170)dx=1500[0.7x33+170x22+170x]5000[ Integrate with respect to x]=1500[0.7(500)33+170(500)22+170(500)]−1500[0.7(0)33+170(0)22+170(0)][ Apply the limits of x]=101003.33333≈101003C(x)=0.7x2+170x+170x∈[0,500]Cavg=Total Cost 500= \int_0^{500} C(x) dx 500=1500∫0500(0.7x2+170x+170)dx=1500[0.7x33+170x22+170x]0500[ Integrate with respect to x]=1500[0.7(500)33+170(500)22+170(500)]−1500[0.7(0)33+170(0)22+170(0)][ Apply the limits of x]=101003.33333≈101003

Therefore, the average cost is Cavg≈101003