A firm has two plants that it may use to produce its output. The first plant has cost function C1 (Q1) = Q1^2 and the second plant has a cost function C2 (Q2) = Q2 + 0.5Q2^2.
a. If total output to be produced, Q1 + Q2, must be Q>0, what is the best way to divide the total output between the two plants in order to generate the lowest total cost for the firm?
b. What is the resulting total cost to produce Q?