Friday

November 28, 2014

November 28, 2014

Posted by **vimal** on Friday, October 8, 2010 at 5:29am.

- engineering -
**drwls**, Friday, October 8, 2010 at 6:06amRevenue = Quantity*Price

R = Q*P = 24Q - .5Q^2

Revenue is a maximum when

dR/dQ = 0

24 -Q = 0

Q = 24 units sold @ a price of P = 12

Profit (P) is

P = R - Q*(AC)= Q*P - Q*(AC)

= 24Q -0.5Q^2 -Q*(Q^2 -8Q +36 +3/Q)

= 24Q -0.5Q^2 -Q^3 +8Q^2 +36Q +3

= -Q^3 +7.5 Q^2 +60Q +3

Set dP/dQ = 0 to solve for the maximum-profit production level, Q.

-3Q^2 +15Q +60 = 0

The positive root is

Q = (-1/6)[-15 -sqrt(289+720)]

Q = 7.8

**Answer this Question**

**Related Questions**

Microeconomics - A perfectly competitive industry has a large number of ...

Maths - Demand function P=50-Q Average Cost 5Q + 40 +10/Q Calculate the firm's ...

q - 2. Given a firm’s demand function, P = 24 - 0.5Q and the average cost ...

ECONOMICS - Q2) Given a firm’s demand function, P = 24 - 0.5Q and the average ...

economics - 2. Given a firm’s demand function, P = 24 - 0.5Q and the average ...

economics - 2. Given a firm’s demand function, P = 24 - 0.5Q and the average ...

economics - 1. Given a firm’s demand function, P = 24 - 0.5Q and the average ...

Microeconomics - A monopoly firm is faced with the following demand function P...

managerial economics - Given a firm’s demand function, P = 24 - 0.5Q and the ...

Microeconomics - A monopoly firm is faced with the following demand function P...