Demand for a product is Q = 100,000 - 1.25P what is the price u charge to maximize revenue

Question

Demand for a product is Q = 100,000 - 1.25P what is the price u charge to maximize revenue

Answer 1

The marginal revenue curve is always decreasing, so at the point where marginal revenue is zero, total revenue will be maximized.  

First find TR

TR=p*q

TR=p(100,000 - 1.25P)

TR=100,0000P - 1.25P^2

Marginal revenue is the derivative of total revenue

MR=TR'=100,000 - 2.5P

Now we set it equal to zero.

100,000 - 2.5P = 0

100,000 = 2.5P

P=100,000/2.5=40,000

Answer 2

Q=100000-1.25P

1.25P=100000-Q

P=100000/1.25 - Q/1.25

P=80000-0.8Q

Substitute the quantity into that