you are the manager at the cadillac division of GM. If the marketing department has estimated that the annual demand for the escalde is Q=100,000-1.25P what price should you charge in order to maximize revenues from sales?
Total revenue is P*Q. So, TR = 100,000P - 1.25P^2.
Take the first derivitive, set it equal to zero and your done.
To maximize revenues from sales, we need to find the price that will yield the highest value for total revenue.
The equation provided is TR = 100,000P - 1.25P^2, where P is the price and Q is the annual demand for the Escalade.
To find the price that maximizes revenue, we can use calculus by taking the first derivative of the total revenue function and setting it equal to zero. This will give us the critical points, where the maximum or minimum occurs.
First, let's differentiate the total revenue function with respect to price (P):
d(TR)/dP = 100,000 - 2.5P
Setting this derivative equal to zero:
100,000 - 2.5P = 0
Solving for P:
2.5P = 100,000
P = 40,000
Therefore, to maximize revenue from sales, you should charge a price of $40,000 for the Escalade.