Here is a linear demand function Q 10 05P Find its price fu

Here is a linear demand function: Q = 10 -0.5P. Find its price function by inverting the demand function. Then find its total revenue function by multiplying through by Q.

P=

TR=

Solution

Q = 10 - .5P

subtracting 10 from both sides

Q - 10 = -.5P

multiplying entire equation by -1

10 - Q = .5P

dividing both sides by .5

20 - Q/.5 = P
price function = 20 - Q/.5

total revenue = (20 - Q/.5 )Q = 20Q - Q^2 /.5