Handwrite the solution for the following question and try and provide explanations for each step for better understanding:

Suppose that a new car costs $$10,000$ and the annual operating cost and resale value of the car

are as shown below. Assuming that one now has bought a new car now, determine a replacement

policy that minimizes the net cost of owning and operating a car for the next six years. Model as

a shortest path problem.

a$)$ Represent the problem on a network and define the nodes, arcs, and arc costs. $(5$ marks$)$

b$)$ Define the decision variables. $(2$ marks$)$

c$)$ Provide the full model. $(3$ marks$)$

Age of Car $($Years$)$ Resale Value $($$$)$ Operating Cost $($$$)$

$17,000\mathrm{.}00300($year $1)$

$26,000\mathrm{.}00500($year $2)$

$34,000\mathrm{.}00800($year $3)$

$43,000\mathrm{.}001200($year $4)$

$52,000\mathrm{.}001600($year $5)$

$61,000\mathrm{.}002200($year $6)$Suppose that a new car costs $$10,000$ and the annual operating cost and resale value of the car

are as shown below. Assuming that one now has bought a new car now, determine a replacement

policy that minimizes the net cost of owning and operating a car for the next six years. Model as

a shortest path problem.

a$)$ Represent the problem on a network and define the nodes, arcs, and arc costs. $(5$ marks$)$

b$)$ Define the decision variables. $(2$ marks$)$

c$)$ Provide the full model. $(3$ marks$)$