Company K wants to determine a replacement policy that minimizes the net costs of owning and operating a machine for the next 6 years (years 1-7).

• The cost to purchase a new machine is $10,000; the purchase cost remains constant throughout the planning horizon.
• The company's policy is
  • not to replace a machine that is less than 2 years old (i.e., to replace a machine it needs to be at least 2 years old)
  • not to keep a machine for more than 5 years (i.e., after 5 years, the machine needs to be replaced so the max-age of a machine should be 5).
• The annual operating costs and salvage value of the machine are shown in the table below.

Age of machine (years)	Annual Operating costs	Salvage value
1	$500	$6,000
2	$1,500	$5,500
3	$2,500	$5,000
4	$3,500	$4,500
5	$4,500	$4,000
6	$5,500	$3,500

Assume that currently (year 1) the company purchases a new machine and that they seek your help determining the minimum cost replacement policy for the next 6 years, i.e. planning horizon until year 7.

Briefly explain how a transshipment network model can be used to solve this problem. Specify:

1. number of nodes, what they represent, and what is the requirement (supply/demand) in each node
2. number of arcs, what they represent, and a general statement about how the cost of each arc is determined

Do NOT WRITE the objective function or any constraints!!!
Use words and/or numerical values to explain (a) and (b) above

use appropriate variables Xij to EXPRESS (write) the flow constraint for YEAR 1

use appropriate variables Xij to EXPRESS (write) the flow constraint for YEAR 3

use appropriate variables Xij to EXPRESS (write) the flow constraint for YEAR 7