Problem $3(30$ pts$)$

You're a freshman in college with a car that could officially breakdown at any moment.

When you graduate in $3$ years, you'll be getting a well$-$paid job, so you'll be able to get a

new $($very reliable$)$ car. Until then, you need to figure out the cheapest plan for making

sure you have a car for the rest of your college years. It might be more economical to

replace your car every year until your graduation or every other year $($or until you

graduate$).$

The table below shows the net cost associated with purchasing a "new" car at the end

of year i and then replacing it at the end of year $j.$ For example, if you were to buy a

"new" car at the end of year $i=1,$ and then replace that car at the end of year $j=3,$ it'll

cost you $$21,000$ overall. Year $0$ represents your current freshman year.

a$)$ Draw the network with nodes and arcs and their associated costs based on the given

table. Hint: each node represents a year. $(5$ pts$)$

b$)$ Formulate this problem as a shortest$-$path $($or "shortest$-$cost$")$ problem, i$.$e$.,$ write out

the LP in full $($no i$\text{'}$s$,$ no j$\text{'}$s$,$ no sigmas$).(15$ pts$)$

c$)$ Solve the LP found in part b using Excel Solver. Then write a sentence saying what

the shortest path is$.$ Provide a screenshot of the solved LP$,$ as well as of the Excel

Solver window $($pre$-$solved$).(10$ pts$)$