Johnson and johnson wants to determine a replacement policy that minimizes their 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; 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 old (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	$7,000
2	$1,500	$6,000
3	$2,500	$5,000
4	$3,500	$4,000
5	$4,500	$3,000
6	$5,500	$2,000

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.

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

number of nodes, what they represent and what is the requirement (supply/demand) in each node

number of arcs, what they represent and 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

b. use appropriate variables Xij to EXPRESS (write) the flow constraint for YEAR 4

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

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