Problem $3$:

Lynn studying abroad has decided that she needs a car for her transportation over the next four years.

With a tight budget, she aims to make the most economical choice. However, she is unsure whether to

buy a used car or a newer model, and she is also considering whether to sell the car after four years.

Below are the key details she needs to evaluate

Purchase

price in $

Cost of car use per year $($$$)$ Car purchase price per year $($$$)$

$1$st $2$nd $3$rd $4$th $1$st $2$nd $3$rd $4$th

Old car $100019002200250028006004002000$

New car $380010001300170023002200160012001000$

If Lynn changes his car within the next four years, he will do it at the end of that year and will take a car

of one of two types. However, he plans to get in the future a newer of that what he gets now. He wants to

find the most appropriate solution.

$1)$ Explain how the given scenario can be structured as a transportation problem, including the key

elements such as sources, destinations, supply, demand, and transportation cost

$2)$ Utilize an appropriate method $($e$.$g$.,$ the Northwest Corner Rule, or Vogel's Approximation$)$ to find an

initial feasible solution for the transportation model.

$3)$ Apply a suitable methodology for solving transportation problems $($the Stepping Stone Method$)$ to

identify the optimal solution that minimizes transportation costs.