Since the formula for R'(c) = 5000 - 200c:
To find where R'(x) > 0: 5000 - 200c > 0 ---> -200c > -5000 ---> c < 25
To find where R'(c) < 0: 5000 - 200c < 0 ---> -200c < -5000 ---> c > 25
The maximum occurs where R'(c) = 0: 5000 - 200c = 0 ---> -200c = -5000 ---> c = 25
When c = 25, the revenue will be R(25) = 5000(25) - 100(25)2 = 62,500