revenue function of x^2+3p=675
To find the revenue function for the equation x^2 + 3p = 675, we need to solve for p in terms of x and then substitute it back into the function.
Step 1: Solve for p in terms of x.
First, isolate p by subtracting x^2 from both sides of the equation:
3p = 675 - x^2
Next, divide both sides of the equation by 3:
p = (675 - x^2) / 3
Step 2: Substitute p back into the revenue function.
The revenue function is generally represented as R(x). In this case, x^2 + 3p = 675 can be rewritten as R(x) = x^2 + 3p.
Now, substitute the value of p obtained in step 1 into the revenue function:
R(x) = x^2 + 3((675 - x^2) / 3)
Simplifying further:
R(x) = x^2 + 3(225 - x^2/3)
R(x) = x^2 + 675 - x^2
R(x) = 675
Therefore, the revenue function for the equation x^2 + 3p = 675 is R(x) = 675.