Question

given the demand function p=1000-Q express TR as a function of Q and hence sketch a graph of TR against Q. What values of Q maximizes total revenue, and what is the corresponding price?

Answer 1

Solution

$TR=P×Q$

$TR=1000Q-Q^{2}$

TR=0 when

$Q=0$ and $Q=50$

Q maximizes TR when the graph is halted or the quantity is halted at Q=25

$TR=100(25)-2(25)^{2}=1250$