Carlton Construction Is Supplying Building Materials for a New Mall

question 37

Essay

Carlton construction is supplying building materials for a new mall construction project in Kansas.Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period.Carlton's supply depot has access to three modes of transportation: a trucking fleet,railway delivery,and air cargo transport.Their contract calls for 120,000 tons delivered by the end of week one,80% of the total delivered by the end of week two,and the entire amount delivered by the end of week three.Contracts in place with the transportation companies call for at least 45% of the total delivered be delivered by trucking,at least 40% of the total delivered be delivered by railway,and up to 15% of the total delivered be delivered by air cargo.Unfortunately,competing demands limit the availability of each mode of transportation each of the three weeks to the following levels all in thousands of tons):
$\begin{array}{cccc}\text { Week } & \text { Trucking Limits } & \text { Railway Limits } & \text { Air Cargo Limits } \\\hline 1 & 45 & 60 & 15 \\2 & 50 & 55 & 10 \\3 & 55 & 45 & 5 \\\hline \text { Costs } \$ \text { per } 1000 \text { tons) } & \$ 20 & \$ 14 & \$ 40\\&0&0&0\end{array}$

Formulate an LP model for this logistics problem.

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Definitions:

Colonization Society

A group or organization established in the early 19th century advocating for the migration of free African Americans to Africa; the American Colonization Society is a prime example.

William Lloyd Garrison

An American abolitionist who was prominent in the anti-slavery movement and is well known for founding and editing the abolitionist newspaper "The Liberator."

Free African-Americans

Individuals of African descent living in the United States who were not enslaved and had certain legal rights, particularly before the Civil War in both the North and the South.