Let's analyze and solve each part step-by-step: --- ## Part 1: Manufacturing Cost Analysis ### Data Summary: | Machine | A | B | C | |---------|---|---|---| | **Unit Production Costs** | | | | | 1 | $13 | $9 | $10 | | 2 | $11 | $12 | $8 | | Machine | A | B | C | |---------|---|---|---| | **Setup Costs** | | | | | 1 | $55 | $93 | $60 | | 2 | $65 | $58 | $75 | | Machine | A | B | C | |---------|---|---|---| | **Hours to produce 1 unit** | | | | | 1 | .4 | 1.1 | .9 | | 2 | .5 | 1.2 | 1.3 | --- ## Part 2: Machine-Job Assignment and Scheduling ### Job times (minutes): | Machine | Job 1 | Job 2 | Job 3 | Job 4 | Job 5 | Setup Time | |---------|--------|--------|--------|--------|--------|------------| | 1 | 42 | 70 | 93 | - | - | 30 | | 2 | - | 85 | - | 45 | - | 40 | | 3 | 58 | - | - | - | 37 | 42 | | 4 | 58 | - | 55 | - | 38 | 75 | | 5 | - | - | - | 60 | 54 | 55 | --- ## Step 1: Determine the minimal total time to complete all jobs ### Approach: - Minimize setup and operation times. - Assign jobs to machines with the least total time (setup + processing). --- ### **Assignment Strategy:** 1. **Job 1:** - Times: Machine 1 (42), Machine 3 (58), Machine 4 (58) - **Best:** Machine 1 (42 mins + setup 30 = 72 mins) 2. **Job 2:** - Times: Machine 2 (85), Machine 4 (55) - **Best:** Machine 4 (55 mins + setup 75 = 130 mins) 3. **Job 3:** - Times: Machine 1 (93), Machine 4 (55) - **Best:** Machine 4 (55 mins + setup 75 = 130 mins) 4. **Job 4:** - Times: Machine 2 (45), Machine 5 (60) - **Best:** Machine 2 (45 mins + setup 40 = 85 mins) 5. **Job 5:** - Times: Machine 3 (37), Machine 4 (38), Machine 5 (54) - **Best:** Machine 3 (37 mins + setup 42 = 79 mins) --- ### **Final assignment:** | Job | Machine | Total time (setup + operation) | |-------|---------|--------------------------------| | 1 | 1 | 72 mins | | 2 | 4 | 130 mins | | 3 | 4 | 130 mins | | 4 | 2 | 85 mins | | 5 | 3 | 79 mins | ### **Total time calculation:** - The overall completion time is dominated by the longest sequence, which involves Machine 4 (jobs 2 and 3) with 130 mins. - The other machines' total times are less or equal. --- ## **Final Summary:** - The **minimum total time to complete all jobs** is approximately **130 minutes**, considering the bottleneck on Machine 4 handling Jobs 2 and 3. - The optimal assignment minimizes setup and operation times by assigning jobs to the most suitable machines based on their individual processing times and setup costs. --- ## **Answer:** **Total number of minutes needed to complete the jobs = \(\boxed{130}\) minutes.**