Carlton Construction Is Supplying Building Materials for a New Mall

question 70

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):
$\begin{array}{cccc}\text { Week } & \text { Trucking Limts } & \text { Ralway Limits } & \text { Air Cargo Limits } \\\hline 1 & 45 & 60 & 15 \\2 & 50 & 55 & 10 \\3 & 55 & 45 & 5 \\\hline \text { Costs }(\$ \text { per } 1000 \text { tons }) & \$ 200 & \$ 140 & \$ 400\end{array}$
Formulate an LP model for this logistics problem.

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Definitions:

Sustainable Incomes

Earnings generated in ways that do not deplete resources or harm the environment, ensuring long-term economic and environmental stability.

Ecology

The branch of biology that studies the interactions among organisms and their environment.

Organisms

Individual living entities that can react to stimuli, reproduce, grow, and maintain homeostasis.

Environment

The surrounding conditions and influences that affect the growth, development, and survival of organisms.