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

Question

Quizplus · Accepted Answer

To ship the largest possible amount using the route from Source 3 to Destination 3, we must consider the remaining supply from Source 3 and the remaining demand at Destination 3. From the table, Source 3 has already shipped all 50 units it supplied, so to use the Source 3 - Destination 3 route, we would need to reallocate some shipments. However, the question asks about the change in the objective function if we could ship using this route without changing supply and demand conditions, which is not directly feasible given the current allocations. The question seems to be theoretical, asking about the impact of shipping an additional amount via this route. If we hypothetically could ship more via Source 3 to Destination 3 without altering the total supply and demand, the cost for shipping each unit is $14. Since Destination 3 has a demand of 70 units and Source 3 has a supply of 50 units, the maximum we could consider shipping via this route (if we ignore the current allocations) is 50 units. The increase in the objective function would be 50 units * $14/unit = $700. However, this option is not listed, suggesting a misunderstanding in the question's premise. Given the options and the scenario, none directly apply to the feasible changes in the objective function based on the provided tables and the constraints of supply and demand. The correct approach to determine the impact on the objective function would involve reallocating shipments to free up capacity for the Source 3 to Destination 3 route, then calculating the difference in cost. However, without specific instructions to reallocate shipments, the direct impact of adding shipments to an already fully allocated supply is not calculable from the given options. The question's setup implies a theoretical addition of shipments to the Source 3 to Destination 3 route, which suggests looking for an increase in cost based on the cost per unit and the amount shipped. However, the calculation provided does not match any of the given options, indicating a possible error in interpreting the question or in the provided options.

Consider the Transportation Problem and Its Optimal Solution in the Tables