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 costs associated with producing in the two plants are MC₁ = 2Q₁ and MC₂ = 4Q₂.How much output should be produced in plant 1 in order to maximize profits? A) 3 B) 6 C) 9 D) 12

Question

Quizplus · Accepted Answer

To maximize profits, we need to produce at the point where marginal revenue (MR) equals marginal cost (MC). First, we need to find the inverse demand function by solving for Q in P = 120-6Q:
P/6 = 20 - Q/6
Q = 120 - 6P
Now we can substitute Q into the expression for marginal revenue (MR):
MR = dP/dQ = 120/6 - 6Q/6 = 20 - Q/6
Setting MR equal to MC for plant 1:
20 - Q/6 = 2Q
Q = 6
Therefore, the optimal output for plant 1 is 6 units.

You Are the Manager of a Firm That Produces Output