Carlton Construction Is Supplying Building Materials for a New Mall

question 13

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):
$\begin{array}{cccc}\text { Week } & \text { Trucking Limits } & \text { Railway Limits } & \text { Air Cargo Limits } \\\hline 1 & 45 & 60 & 15 \\2 & 50 & 55 & 10 \\3 & 55 & 45 & 5 \\\hline \text { Costs } \$ \text { per } 1000 \text { tons) } & \$ 20 & \$ 14 & \$ 40\\&0&0&0\end{array}$

The following is the LP model for this logistics problem.
$\text { Let }$



What values would you enter in the Risk Solver Platform RSP)task pane for the cells in this Excel spreadsheet implementation of this problem?
Objective Cell: Variables Cells: Constraints Cells:

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Definitions:

Marginal Costs

The increase in total cost that arises from an extra unit of production.

Fixed Factors

Inputs in production that cannot be altered in the short term, such as buildings and machinery.

Output

The amount of goods and services produced by a business, industry, or economy.

Marginal Cost

The cost added by producing one additional unit of a product or service, important for decision-making in resource allocation.