Question: A production facility experiences 1000 units of demand increase per year for a foreseeable future. The management has an option to either add a machine with production capacity of 2000 units every 2 years for a cost of $3000 per machine or a machine with a production capacity of 4000 units every 4 years at a cost of $5000 per machine. The company uses a discount rate of 10% per year, compounded continuously.
a. Determine the better of the two alternatives
b. Find the parameters k and a associated with the economy of scale function f(y) = ky^a assuming that the manufacturer of the machine can produce a machine to any capacity y units per year at a cost off(y).
c. Find the optimal capacity y*, optimal time interval between capacity increments, and the associated present worth of all capacity increments assuming the economy of scale function determined in part b.