To find the profit equation, you'll need to subtract the cost equation from the revenue equation. Given:
Revenue equation (R) = 2000x - 10x^2
Cost equation (C) = 2000 + 500x
The profit equation (P) can be expressed as:
P(x) = R(x) - C(x)
P(x) = (2000x - 10x^2) - (2000 + 500x)
Now, simplify the equation:
P(x) = 2000x - 10x^2 - 2000 - 500x
Combine like terms:
P(x) = (2000x - 500x) - 10x^2 - 2000
P(x) = 1500x - 10x^2 - 2000
So, the profit equation for this business is:
P(x) = -10x^2 + 1500x - 2000