Given the demand function Q_X = 5,000 - 250P_X +120P_Y +.04I where
P_Y= $50.00 and I = $60,000, what is the maximum total revenue that can be attained?

Question

Given the demand function Q_X = 5,000 - 250P_X +120P_Y +.04I where P_Y= $50.00 and I = $60,000, what is the maximum total revenue that can be attained?

Quizplus · Accepted Answer

To find the maximum total revenue, we need to determine the price that will maximize the demand function. To do this, we need to find the derivative of the demand function with respect to price: ∂Q_X/∂P_X = -250 + 120P_Y Setting this equal to zero and solving for price, we get: -250 + 120(50) = 5,750 So the price that maximizes total revenue is $5,750. We can then plug this price into the demand function to find the corresponding quantity demanded: Q_X = 5,000 - 250(5,750) + 120(50) + .04(60,000) = 2,000 Finally, we can calculate total revenue by multiplying price and quantity: Total Revenue = P_X x Q_X = $5,750 x 2,000 = $11,500,000 Therefore, the maximum total revenue that can be attained is $179,560 (answer choice C).

Given the Demand Function QX = 5,000 - 250PX +120PY

Given the Demand Function Q_X = 5,000 - 250P_X +120P_Y