Find profit function P(x) and the number of units x to produce to maximize the profit

C(x) = 23x^2 + 500x
R(x) = (1/3)x^3 - 12x^2 +1500x

explain with work please :)

P(x) = R(x) - C(x)

P(x) = (1/3)x^3 - 12x^2 +1500x - 23x^2 - 500x

P(x) = (1/3)*x^3 - 35*x^2 + 1000*x

diff((1/3)*x^3 - 35*x^2 + 1000*x, x) = x^2 - 70*x + 1000

solve(x^2 - 70*x + 1000 = 0)

(x - 50)*(x - 20) = 0

x1 = 50, x2 = 20

f(x):=( (1/3)*x^3 - 35*x^2 + 1000*x)

f(50) = 12500/3

f(20) = 26000/3 ≈ 8,667; to produce 20 units guarantees the maxim profit!