Microeconomics 2nd Edition by Douglas Bernheim

Exercise 3

A firm has two production plants. The cost function of plant 1 is C 1 ( Q 1 ) = 10 Q 1 + ( Q 1 ) 2 where Q 1 is the number of units of output produced in plant 1. The cost function of plant 2 is C 2 ( Q 2 ) = 10 Q 2 + 4( Q 2 ) 2 where Q 2 is the number of units of output produced in plant 2. If the firm wants to produce Q total units of output, what is the allocation of production across the two plants that minimizes its cost