The maintenance cost of capital equipment-machineries, tools, and buildings- increases as they get older. Assume the maintenance cost of capital equipment, M(t), for a manufacturer is given by M(t) = 30 t3 + 5000 t + 400 where t is years of equipment in service.
(a) Write the average and marginal functions of the maintenance cost.
(b) Calculate M(5) and M!(5). What is the interpretation of M!(5)?