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University of Colorado, Boulder *

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4820

Subject

Computer Science

Date

Feb 20, 2024

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Uploaded by MegaJellyfishPerson511

) - (50pts) Union Pacific 1s looking to reposition some of its empty railcars. The company currently has an excess of 260 empty railcars in Denver. 430 empty railcars n Houston. and 310 empty railcars mn Chicago. Shortages include 320 cars m Los Angeles. 280 in Seattle and 400 in San Francisco. The cost to transfer a single railcar between each city 1s shown in the table below. LOS ANGELES SEATTLE SAN FRANCISCO DENVER | $439 $396 $910 HOUSTON | $296 $434 $133 CHICAGO | $131 $184 $479 a) Formulate a linear programming model to minimize the cost of repositioning the empty railcars. Clearly define the decision variables, the objective function. and the constraints. b) Create a spreadsheet model for this problem and solve it using Solver. What 1s the optimal solution? ¢) Suppose now that at most 200 railcars can be transferred between each pair of cities. How will this impact the optimal solution?

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