Question 383066
The price is :  C (x)= 1/20x^2-4/5x+9 1/5 thousand $ for x hundred items.
 
TO find the minimal price, need to find the cost where it's variation is zero, and for which any change would imply an increase in price, hence the variation is positive in price for any variation in item numbers : 
 
Price variation (derivative) : C'(x) = 1/10x-4/5 = 0 => x = 8 hundred items
 
Variation of the latter : C''(x)=1/10 > 0 => hence any variation at x=8 imply an increase in the cost, this minimal cost being : C(8)=64/20-32/5+9+1/5=(16-32+45+1)/5=30/5=6 thousand $.