A Company Needs to Ship 100 Units from Seattle to Denver

Essay

A company needs to ship 100 units from Seattle to Denver at the lowest possible cost. The costs associated with shipping between the cities are listed below. Also, the decision variable associated with each pair of cities is shown next to the cost.
$$\begin{array}{l}\text { Ta }\\\begin{array} { l c c c c } \text { From } & \text { Portland } & \text { Spokane } & \text { Salt Lake City } & \text { Denver } \\\hline \text { Seattle } & 100 \left( X _ { 12 } )\right. & 500 \left( X _ { 13 } \right) & 600 \left( X _ { 14 } \right) & - \\\text { Portland } & - & 350 \left( X _ { 23 } \right) & 300 \left( X _ { 24 } \right) & - \\\text { Spokane } & - & - & 250 \left( X _ { 34 } \right) & 200 \left( X _ { 35 } \right) \\\text { Salt Lake City } & - & - & - & 200 \left( X _ { 45 } \right)\end{array}\end{array}$$ Write out the LP formulation for this problem.