Question

Assume that it costs Apple approximately
C(x)= 14,400+100x+0.01x^2
dollars to manufacture x 32GB ipods in a day. How many ipods should be manufactured in order to minimize average cost?
_________ ipods per day

what is the resulting average cost of an ipod?
_________

Answer 1

Average cost is the cost function divided by x; so average cost =22500/x +100 +.01 x. Take the derivative: 
A'= -22500/x^2 +..01. Set that to 0; so 01 =22500/x^2; 
.01 x^2 =22500; 
x^2 = 2250000 
x=1500. You should manufacture 1500 per day. 
Now use 1500 in your equation for average cost: 
22500/1500 +100 +.01 (1500) =15+100+15 =130.

so $130.00