Consider a firm that is using two plants, A and B, with these MC functions 

MC_A = 10 + 0.01Q_A           and    MC_B = 4 + 0.03Q_B 

a. Find the inverse marginal cost functions. 

b. Set MC_A = MC_T and MC_B = MC_T, and find the algebraic sum Q_A + Q_B = Q_T. 

c. Take the inverse of the horizontal sum in part b to get the total marginal cost (MCT) expressed as a function of total output (Q_T). 

d. Beyond what level of output will the firm use both plants in production? 

e. If the manager of this firm wished to produce 1,400 units at the least possible total cost, should 700 units be produced in each plant? Why or why not? If not, what should the allocation be? 

f. Draw a graph of MC_A, MC_B, and MC_T. Check your algebraic derivation of total mar ginal cost with your graph. Check your answer to part e.