Question 1054875
 5300=500+1400x-100x2
100x^2-1400x+4800=0
x^2-14x+48=0, after dividing by 100.
(x-6)(x-8)=0
x=6, 8, or 600, 800 items.  Maximum x is -b/2a=-1400/-200=7
check both
C6=500+8400-3600=$5300
C8=500+11200-6400=$5300
{{{graph(300,300,-10,10,-1000,6000,500+1400x-100x^2)}}}