A student 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 evaluateIf the students changes her car within the next four years, she will do it at the end of that year and will take a car of one of two types. However, she plans to get in the future a newer of that what she gets now. she 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, 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. A student 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

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|$l$|$l$|$l$|$l$|$l$|$l$|$l$|\}$

$\backslash$hline & $\backslash$multirow$\{4\}\{*\}\{\backslash$begin$\{$tabular$\}\{$l$\}$

Purchase $\backslash \backslash$

price in $\backslash$$

$\backslash$end$\{$tabular$\}\}$ & $\backslash$multicolumn$\{4\}\{|$l$|\}\{$ Cost of car use per year $(\backslash$$$)\}$ & $\backslash$multicolumn$\{4\}\{$l$|\}\{$ Car purchase price per year $(\backslash$$$)\}\backslash \backslash$

$\backslash$cline $\{3-10\}$ & & $1$st & $2$nd & $3$rd & $4$th & $1$st & $2$nd & $3$rd & $4$th $\backslash \backslash$

$\backslash$hline Old car & $1000$ & $1900$ & $2200$ & $2500$ & $2800$ & $600$ & $400$ & $200$ & $0\backslash \backslash$

$\backslash$hline New car & $3800$ & $1000$ & $1300$ & $1700$ & $2300$ & $2200$ & $1600$ & $1200$ & $1000\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

If the students changes her car within the next four years, she will do it at the end of that year and will take a car of one of two types. However, she plans to get in the future a newer of that what she gets now. she 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, 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.