This problem is a classic "assignment problem" in operations research, where we aim to assign resources (1, 2, 3, 4) to jobs (A, B, C, D) in a way that minimizes the total time spent (or cost).

To solve it optimally, we typically apply the Hungarian Algorithm or manually calculate based on the minimum total hours by checking all possible assignments.

Resource-to-Job Table

Now let’s determine the optimal assignment step by step:

Steps:

1. Look for the lowest time values for each resource, ensuring no conflicts in assignment.
2. Avoid overlapping assignments for any resource and job.

Assignment:

• Resource 1 → A (5 hours)
• Resource 2 → C (5 hours)
• Resource 3 → D (7 hours)
• Resource 4 → B (6 hours)

Total Hours:

$5 (1 \to A) + 5 (2 \to C) + 7 (3 \to D) + 6 (4 \to B) = 23$

Correct Answer:

1 to A; 2 to C; 3 to D; 4 to B.

This corresponds to the last option.

Would you like a more detailed explanation or further assistance with the Hungarian Algorithm?

Related Questions:

1. What is the Hungarian Algorithm, and how is it used in assignment problems?
2. How can assignment problems be solved using matrices?
3. What happens if the costs (or times) are not square (e.g., 3 resources and 4 jobs)?
4. How is the optimal solution verified in assignment problems?
5. Are there variations of the assignment problem (e.g., maximization instead of minimization)?

Tip:

Always ensure that assignments satisfy the constraints (e.g., no resource assigned to more than one job) while minimizing (or maximizing) the total cost/time.