Average and marginal cost curves of the firm

Question

Task 1: Epren manufactures engine parts for an automobile manufacturer. It operates 2 plants, which have the following production functions:

Plant A: Q_a = 30S_a – 0.25 S_a²

Plant B: Q_b = 40S_b – 0.50S_b²

where Q_a is the unit output from plant A, Q_b is the unit output from plant B and S_a and S_b are the units of the variable factor steel used, respectively at plant A and B. 

a) Suppose the steel availability is 30 units.  What is the optimal allocation between the two plants?

b) A sudden supplier problem reduces availability of steel to plant B by 10 units.  How should Epren reallocate steel between the plants?  Explain.

Task 2: Explain how the following events will affect the average and marginal cost curves of the firm.

a. An increase in lease payments.

b. A decrease in utility cost.

c. Stricter environmental regulations requiring installation of scrubbers on smokestacks.

d. An increase in the corporate profit tax.

e. An increase in learning on the part of labor.