$5)$ Railroad Car Rumba $-$ The Rock Island Railroad $($RIRA$)$ has $100$ empty railcars at

its Sioux City rail yards and $150$ rail cars at its North Platte location available for retrofitting for a new project. Ultimately, RIRA must get $75$ retro$-$fitted cars to Chicago, $85$

retro$-$fitted cars to Peoria, and $55$ retro$-$fitted cars to St Louis.

To retro$-$fit the cars, two different stages of maintenance must be performed on the rail

cars. Stage $1$ retro$-$fitting occurs either at Lincoln, Omaha or Des Moines. Stage $2$ retrofitting occurs at Davenport, IA or Kansas City. Cars must pass first through Stage $1,$ then

Stage $2,$ before arriving at the final destination.

We are not interested in retro$-$fitting costs at the $5$ different maintenance locations. Our

goal is to find the least distance way to transform the railcars and get them $($in their retrofitted format$)$ to Chicago, Peoria and St$.$ Louis.

Stage $1$ and Stage $2$ locations have capacities for retro$-$fitting. They are listed below.

Omaha Lincoln KC

GI $148103274$

Columbus $8378256$

Nebr City $4552128$

Location Capacity Stage

Lincoln $1151$

Omaha $901$

Des Moines $501$

Davenport, IA $952$

Kansas City $1352$

Relevant distances are shown below. Using an appropriate linear programming model,

find the optimal way of satisfying the rail car transformation problem for RIRA.

Explicitly explain why your solution says in terms of cars transportation.

Lincoln Omaha

Des

Moines Chicago Peoria StLouis

Sioux City $188162209$

N Platte $214248372$

Davenport $32028115615276203$

Kcity $1631671775292852345)$ Railroad Car Rumba $-$ The Rock Island Railroad $($RIRA$)$ has $100$ empty railcars at

its Sioux City rail yards and $150$ rail cars at its North Platte location available for retrofitting for a new project. Ultimately, RIRA must get $75$ retro$-$fitted cars to Chicago, $85$

retro$-$fitted cars to Peoria, and $55$ retro$-$fitted cars to St Louis.

To retro$-$fit the cars, two different stages of maintenance must be performed on the rail

cars. Stage $1$ retro$-$fitting occurs either at Lincoln, Omaha or Des Moines. Stage $2$ retrofitting occurs at Davenport, IA or Kansas City. Cars must pass first through Stage $1,$ then

Stage $2,$ before arriving at the final destination.

We are not interested in retro$-$fitting costs at the $5$ different maintenance locations. Our

goal is to find the least distance way to transform the railcars and get them $($in their retrofitted format$)$ to Chicago, Peoria and St$.$ Louis.

Stage $1$ and Stage $2$ locations have capacities for retro$-$fitting. They are listed below.

Omaha Lincoln KC

GI $148103274$

Columbus $8378256$

Nebr City $4552128$

Location Capacity Stage

Lincoln $1151$

Omaha $901$

Des Moines $501$

Davenport, IA $952$

Kansas City $1352$

Relevant distances are shown below. Using an appropriate linear programming model,

find the optimal way of satisfying the rail car transformation problem for RIRA.

Explicitly explain why your solution says in terms of cars transportation.

Lincoln Omaha

Des

Moines Chicago Peoria StLouis

Sioux City $188162209$

N Platte $214248372$

Davenport $32028115615276203$

Kcity $163167177529285234$