Derivatives in Word Problem Format

a manufacturer can produce tape recorders at a cost of $20 apiece. It is estimated that if the tape recorders are sold for x dollars apiece, consumers will buy 120-x of them each month. Use calculus to determine the proce at which the manufacturer's profit will be the greatest.

I set up the problem like this (please double check this)

R=20x(120-x)

R=2400x - 20x^2

R'(x) = 2400-40x

highest point

0=2400-40x

40x=2400

x=60

Thanks for all your help, sometimes I forget to say Thank You.