Answer to Question #101404 in Microeconomics for Yusuf musa

Question

1. if a firm revenue course function is given as R=250Q + 3Q2 C= 150 - 5Q derive the maximization output and profit acqiured to the firm. 2. supposed a firm has the following information, the course of machinery factory plant amounted to 50,000. if it variable function is given below; 20x - 3x2 and price per eggs is given as 250 - 15x. what is the profit function of the firm?

Answer 1

profit =R(X)-C(X)

R=250Q+3Q²

C=150-5Q, Profit =250Q+3Q²-150-5Q

=3Q²+250Q-5Q-150

now use the quadratic equation to solve the function

3Q²+245Q-150=0

3Q²+245Q=150

0=( x-b/2)²=150

our b is 245

(x-245/2)²=150

find the square roots for both sides in order to remove the square

now we have (x-245/2)=150

x-122.5=150

x=150+122.5

x=272.5

now we find the square root of the above answer =16.5

x=122.5+16.5 or 122.5-16.5

x=139 or 106

take any from 139 or 106

take 106 to solve the above equation for us to get the profit

p=3Q²+245Q-150

where Q =106

3(106)²[phone]

P=33708+25970-150

PROFIT = 59,678

2.PROFIT FUNCTION OF A FIRM

revenue = 20x-3x2

cost=250-15x

therefore profit =R(X) - C(X)

20X-3X2-250-15X

-3X2+20X-15X-250

=-3X2+5X-250

50,000=-3X2+5X-250

-3X2+5X-250=0

-x2+5x=250

now we use the quadratic equation to solve this

(x-b/2)²

our b =5

(x-5/2)²=250

square roots for both sides

x-2.5=250

x-2.5=15.8

x=15.8+2.5

x=18.3 or 15.8-2.5 =13.3