Question 979471
 12,500 = - 100 x^2 + 2500x +1000.
100x^2-2500x+11500=0.  
divide by 100
x^2-25x+115

x=(1/2)* 25 +/- sqrt (625-460); sqrt 165=12.845

=(1/2) 37.845=19 rounded
=(1/2) 12.155=7 rounded up.

try 18, because there are two positive roots.
-32400+(2500*18)+1000=-32400 + 45000=12,600

Try 7, because the curve is rising here.
12500=-4900+17,500+1000;  second part=13,600.  If I use 6, -3600+16000=12,400

The graph shows how close the profit is to 12,500, not the profit itself.

Note: this is not the maximum profit, which would occur at 12.5 or 12 ,13 as nearest to that.

{{{graph(300,300,-20,20,-10,13000,-100(x^2)+2500x-11500)}}}