Consider the Transportation Problem and Its Optimal Solution in the Tables

question 89

Multiple Choice

Consider the transportation problem and its optimal solution in the tables below. The cell Source 3 - Destination 3 is currently empty. What would be the change in the objective function if the largest possible amount were shipped using that route, leaving all the supply and demand conditions unchanged?
$\begin{array}{|l|r|r|r|r|r|}\hline \text { COSTS } & \text { Dest. 1 } & \text { Dest. 2 } & \text { Dest. 3 } & \text { Dest. 4 } & \text { Supply } \\\hline\text { Source 1 } & 12 & 18 & 9 & 11 & 105 \\\hline \text { Source 2 } & 19 & 7 & 30 & 15 & 145 \\\hline \text { Source 3 } & 8 & 10 & 14 & 16 & 50 \\\hline\text { Demand } & 80 & 60 & 70 & 90 & 300/300 \\\hline & & & & & \\\hline \text { Shipments } & \text { Dest. 1 } & \text { Dest. 2 } & \text { Dest. 3 } & \text { Dest. 4 } & \text { Row Total } \\\text { Source 1 } & 30 & 0 & 70 & 5 & 105 \\\text { Source 2 } & 0 & 60 & 0 & 85 & 145 \\\text { Source 3 } & 50 & 0 & 0 & 0 & 50 \\\text { Col. Total } & 80 & 60 & 70 & 90 & 300/300 \\\hline\end{array}$

• A) 0
• B) fifty units
• C) a decrease of $9
• D) an increase of $450
• E) an increase of $630

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Definitions:

Pareto Optimal

A Pareto optimal outcome is one in which it is impossible to make any individual better off without making at least one individual worse off.

Marginal Rate of Substitution

The rate at which one good can be substituted for another by a consumer without affecting their overall utility level.

Wheat

A cereal grain grown worldwide and a staple food for a large part of the world's human population, used to make products like bread, pasta, and couscous.

Milk

A nutrient-rich fluid produced by the mammary glands of mammals, commonly consumed by humans and used in a variety of food products.