Production process of a product consists of 3 stages and is in a steady state.

---->A -> buffer area -> B ---> buffer area ----> C ->

each stage has a special machine type A B C. complete product goes through all the 3 stages. Currently the firm has one machine at each stage. Monthly demand for product is 100 units and unit profit margin of the product is $250. Below is a summar of info on machines

monthly prod rate 40(A) 90(B) 60(C)

cost to buy machine $100K(A) $160K(B) $250K(C)

assume cash flow compound monthly to perpetuity and annual cost of capital is 12%

Firm considers adding capacity to this process. When additional machine is purchased, it icreases the production rate of that stage by prod rate of new machine.

How Many additional machines at each stage should be bought if goal is to maximize the present value of the profit