To minimize the total cost for the job assignments, we need to apply a method like the Hungarian Algorithm or simply inspect the cost matrix to find the lowest cost per job.

Table of Costs:

Strategy:

We will assign each job to the machine that minimizes the total cost while ensuring that each job is done by a different machine. Let's go step by step:

1. Job A:

   • Machine X: 4
   • Machine Y: 6
   • Machine Z: 8
   • Lowest cost is 4 on Machine X.

2. Job B:

   • Machine X: 2
   • Machine Y: 3
   • Machine Z: 4
   • Lowest cost is 2 on Machine X, but Machine X is already assigned to Job A. So, we pick the second lowest: 3 on Machine Y.

3. Job C:

   • Machine X: 4
   • Machine Y: 8
   • Machine Z: 5
   • Lowest cost is 5 on Machine Z (since Machine X and Y are already assigned).

Final Assignment:

• Job A → Machine X (cost: 4)
• Job B → Machine Y (cost: 3)
• Job C → Machine Z (cost: 5)

Minimum Total Cost:

$4 + 3 + 5 = 12$

This assignment minimizes the total cost to 12.

Would you like more details or have any questions? Here are five related questions to consider:

1. What is the Hungarian Algorithm and how does it work?
2. How would the cost change if there were more jobs than machines?
3. Can this method be used for larger cost matrices, and what are the challenges?
4. How does optimization change if machines can do multiple jobs?
5. Can linear programming be used to solve this kind of assignment problem?

Tip: The Hungarian Algorithm is a powerful tool for solving assignment problems efficiently and ensuring minimal cost.