You are the manager of a firm that produces output in two pl

You are the manager of a firm that produces output in two plants. The demand for your firm\'s product is P = 120 - 6Q, where Q = Q1 + Q2. The marginal cost associated with producing in the two plants are MC1 = 4Q1 and MC2 = 2Q2. How much output should be produced in plant 1 in order to maximize profits?

Select one:

a. 6.

b. 3.

c. 12.

d. 9.

Solution

TR=(120-6Q)*Q=120Q-6Q^2

MR=120-12Q

MR=120-12Q1-12Q2

We know that MR=MC for profit maximisation

therefore

MR=MC1 and MR=MC2

120-12Q1-12Q2=4Q1

120-12Q2=8Q1

12Q2+8Q1=120.....Eq 1)

120-12Q1-12Q2=2Q2

120-12Q1=10Q2

12Q1+10Q2=120.......Eq 2)

Multiplying equation1 eith 6 and equation 2 with 4 then substractwe get

72Q2+48Q1=720

48Q1+40Q2=480

32Q2=240

Q2=7.5 and Q1=(480-40Q2)/48=(480-7.5)/48=9

Hence Option D is correct response