NBL is a monopoly producer of baseballs. Suppose that the demand for baseballs is given as
Q=40,000-20,000P
Where P is in dollars per baseball. Baseballs can be produced in a facility in Southeast Asia where the total cost function is:
C(Q1)=(1/20,000)(Q1)2
Baseballs can also be produced in a facility in Latin America where the total cost function is:
C(Q2)=(1/40,000)(Q2)2

What principles and insights from microeconomic theory guide the profit-maximizing monopolist when allocating the firm's total production of baseballs into the two geographically distinct plant facilities?

Illustrate geographically the monopolist's problem. What is the monopolist's optimal total production level over both production facilities, and what is the optimal production allocation for baseballs in the two distinct production facilities? Is any output produced in the Southeast Asia production facility, given that its cost curve is higher than that for Latin America, at all common output levels? Why or why not?

What is the optimal price of baseballs (Show calculations)? How many are produced in Southeast Asia? How many in Latin America? What are the total profits to NBL?