suppose that unit price p in dollars for a quantity demanded X of a certain product of a company is given by p=-0.08+620 (0 <x <14,000).
find the revenue function. Find marginal revenue function.
fix typo
revenue = p*demand
then take derivative.
Can you format the revenue function for me based off my problem. I had got -0.08x^2 + 620. Check to see if I'm correct
Never mind I got it now
To find the revenue function, we need to multiply the unit price (p) by the quantity demanded (X).
The unit price equation is given as:
p = -0.08X + 620
To find the revenue function, we substitute this equation into the equation for revenue (R):
R = p * X
Substituting the value of p from the given equation:
R = (-0.08X + 620) * X
Expanding and simplifying:
R = -0.08X^2 + 620X
Therefore, the revenue function is R = -0.08X^2 + 620X.
To find the marginal revenue function, we need to differentiate the revenue function with respect to X. Since the revenue function is quadratic, we differentiate it using the power rule of differentiation.
Differentiating R = -0.08X^2 + 620X:
dR/dX = -0.16X + 620
Therefore, the marginal revenue function is dR/dX = -0.16X + 620.
Note: The derivative of the revenue function represents the rate of change of revenue with respect to the quantity demanded, which is the marginal revenue. In this case, the marginal revenue is a linear function of X.