problem two plants production a firm has two

Question

Problem: Two plants production.

A firm has two plants that produce the same good. The cost functions for the two plants are
VC(y₁) = (y₁)²/2
VC(y₂) = y₂
where y₁ and y₂ are quantities of output produced in each plant.

a. If the firm wants to produce one unit of output at minimum cost, how much should it produce in each plant? If it wants to produce two units of output?

b. Now consider an arbitrary quantity of output y. To minimize costs, how should the firm produce its output in each plant? (Hint: draw the two cost curves on the same graph.)

c. What does the firm's cost function look like? Draw it on the graph.

d. What are the average and marginal cost functions? Draw them on separate graphs.