The Following Table Shows the Unit Shipping Cost Between Cities,the

question 46

Essay

The following table shows the unit shipping cost between cities,the supply at each source city,and the demand at each destination city.The Management Scientist solution is shown.Report the optimal solution. $$\begin{array} { l | c c c c | c } &&\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad { \text { Destination } } & \\{ \text { Source } } & \text { Terre Haute } & \text { Indianapolis } & \text { Ft. Wayne } & \text { South Bend } & \text { Supply } \\\hline \text { St. Louis } & 8 & 6 & 12 & 9 & 100 \\\text { Evansville } & 5 & 5 & 10 & 8 & 100 \\\text { Bloomington } & 3 & 2 & 9 & 10 & 100 \\\hline { \text { Demand } } & 150 & 60 & 45 & 45 &\end{array}$$ TRANSPORTATION PROBLEM
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OBJECTIVE: MINIMIZATION
SUMMARY OF ORIGIN SUPPLIES
******************************** $$\begin{array} { c c } \text { ORIGIN } & \text { SUPPLY } \\-----&-----\\1 & 100 \\2 & 100 \\3 & 100\end{array}$$ SUMMARY OF DESTINATION DEMANDS
*************************************** $$\begin{array} { c c } \text { DESTINATION } & \text { DEMAND } \\\hline 1 & 150 \\2 & 60 \\3 & 45 \\4 & 45\end{array}$$ SUMMARY OF UNIT COST OR REVENUE DATA
********************************************* $$\begin{array} { c c c c r } \text { FROM } && { \text { TO DESTINATION } } \\\text { ORIGIN } & 1 & 2 & 3 & 4 \\\hline1 & 8 & 6 & 12 & 9 \\2 & 5 & 5 & 10 & 8 \\3 & 3 & 2 & 9 & 10\end{array}$$ OPTIMAL TRANSPORTATION SCHEDULE
**************************************** $$\begin{array} {c } \text { SHIP } & & & \\\text { FROM } && { \text { TO DESTINATION } } \\\text { ORIGIN } & 1 & 2 & 3 & 4 \\ \ldots\ldots \ldots & \ldots & \ldots & \ldots & \ldots \\1 & 0 & 10 & 45 & 45 \\2 & 100 & 0 & 0 & 0 \\3 & 50 & 50 & 0 & 0\end{array}$$ TOTAL TRANSPORTATION COST OR REVENUE IS 1755

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Definitions:

Express Authority

The explicit power given by a party to someone, allowing them to act on the party's behalf, often found in legal and organizational contexts.

Implied Authority

Authority of an agent that is not explicitly stated but is implied by the agent's actions or the circumstances of the task.

Terminate

To bring something to an end or conclude its operation.

Agency Relationship

A legal relationship in which one party, the agent, acts on behalf of another party, the principal, with the principal's consent.