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?

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

The variables should add up to equal 1