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:

CRA

Canada Revenue Agency, the federal agency that administers tax laws for the Government of Canada and for most provinces and territories.

Lease Agreement

A contract specifying the terms under which one party agrees to rent property owned by another party.

Economic Life

Refers to the duration over which an asset remains productive or useful for its intended purpose.

Capital Lease

A lease agreement that is considered a purchase of an asset for accounting purposes, because it transfers substantially all the risks and rewards of ownership.