Asked by Carmia Mattox on Jun 05, 2024

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Three jobs are to be assigned to three machines. Cost for each job-machine combination appears in the table below. Perform the first two steps of the assignment method (subtract the smallest number in each row and subtract the smallest number in each column; then cover with straight lines) . At this point in the problem-solving process  Machine A  Machine B  Machine C  Tob 1 11146 Tob 2 81011 Job 3 9127\begin{array} { | l | l | l | l | } \hline & \text { Machine A } & \text { Machine B } & \text { Machine C } \\\hline \text { Tob 1 } & 11 & 14 & 6 \\\hline \text { Tob 2 } & 8 & 10 & 11 \\\hline \text { Job 3 } & 9 & 12 & 7 \\\hline\end{array} Tob 1  Tob 2  Job 3  Machine A 1189 Machine B 141012 Machine C 6117

A) the row for Job 1 contains the values 5, 6, and 0.
B) calculations are complete, and the problem is ready for an optimal set of assignments.
C) the column for Machine B indicates that it should be retired.
D) Job 1 should be performed on Machine B.
E) Job 1 should be performed on Machine A.

Assignment Method

The assignment method is a mathematical technique used for allocating resources or tasks to units in an efficient manner, often used in operations research.

Job-Machine Combination

A matching process in operations management that involves assigning specific jobs to specific machines or workstations, optimizing for efficiency and output.

Optimal Assignments

The best possible allocation of tasks, resources, or personnel to jobs, projects, or roles based on specific criteria to maximize efficiency or outcome.

  • Apply techniques for loading, delegating tasks, and scheduling to advance the optimization of resource allocation.
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Tushar BhushanJun 10, 2024
Final Answer :
A
Explanation :
EFirst, subtract the smallest number in each row from all elements of that row. For Job 1, subtract 6 (the smallest number) from all elements, resulting in 5, 8, and 0. For Job 2, subtract 8 (the smallest number) from all elements, resulting in 0, 2, and 3. For Job 3, subtract 7 (the smallest number) from all elements, resulting in 2, 5, and 0. Then, subtract the smallest number in each column from all elements of that column. The smallest numbers in the columns are now 0, 2, and 0, respectively. After subtraction, the table looks like this: Machine AMachine BMachine CJob 1560Job 2003Job 3230\begin{array}{|l|l|l|l|}\hline& \text{Machine A} & \text{Machine B} & \text{Machine C} \\\hline\text{Job 1} & 5 & 6 & 0 \\\hline\text{Job 2} & 0 & 0 & 3 \\\hline\text{Job 3} & 2 & 3 & 0 \\\hline\end{array}Job 1Job 2Job 3Machine A502Machine B603Machine C030 This confirms choice A, as the row for Job 1 contains the values 5, 6, and 0 after the first two steps.Choice E is incorrect based on the given table and the steps performed; the assignment method does not suggest Job 1 should be performed on Machine A at this stage. The method involves minimizing the cost, and the choice does not directly follow from the steps described. The correct interpretation of the table after the first two steps does not inherently suggest an optimal assignment without further analysis.