Answer to Question #298536 in Calculus for saNDY

Question

A firm faces the demand function

P = 190 - 0.6Q and the total cost function

C = 40 + 30Q + 0.4Q2

Answer 1

a)  What output will maximize profit?

$MC=p$ $MC=C'(q)=30+0.8q$

Then

$30+0.8q=190-0.6q$ $q=114$

b) What output will maximize total revenue?

$TR=pq$ $TR=190q-0.6q^2$ $TR'(q)=190-1.2q$ $TR'(q)=0=>190-1.2q=0$ $q=158$

c) What will the output be if the firm makes a profit of 4,760?

$TR-TC=190q-0.6q^2-(40+30q+0.4q^2)$ $=160q-q^2-40$

$160q-q^2-40=4760$ $q^2-160q+4800=0, q\ge 0$ $(q-80)^2=1600$ $q_1=80+40=40, q_2=80-40=40$