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Nested Schedule Optimization Beginner-Intermediate Worksheet: Focus on common variations practice Nested Schedule Optimization BEGINNER INTERMEDIATE

Level up your Nested Schedule Optimization skills! You're at Worksheet 4 of 10 (33% through this series). This step-up challenge worksheet features 20 beginner-intermediate-level problems with a focus on common variations practice. Topics covered: nested schedule optimization for competitive exams, how to solve nested schedule optimization, nested schedule optimization tricks.

📝 Worksheet 4 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner Intermediate level

What you'll learn in this worksheet:
Your progress through Nested Schedule Optimization
Worksheet 4 of 10 (33% complete)

Question 1

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 2 - Assemble: 45 min on Line 2 - Package: 15 min on Line 3 **Product Y:** - Cut: 20 min on Line 2 - Assemble: 60 min on Line 3 - Package: 20 min on Line 2 **Product Z:** - Cut: 40 min on Line 2 - Assemble: 30 min on Line 2 - Package: 25 min on Line 2 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 0 minutes
- Line 2: 210 minutes
- Line 3: 75 minutes

2. Identify bottleneck: The line with maximum load = Line 2
3. Bottleneck load: 210 minutes

Answer: Line 2 (210 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.

Question 2

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 3 - Assemble: 45 min on Line 2 - Package: 15 min on Line 3 **Product Y:** - Cut: 20 min on Line 3 - Assemble: 60 min on Line 3 - Package: 20 min on Line 2 **Product Z:** - Cut: 40 min on Line 3 - Assemble: 30 min on Line 3 - Package: 25 min on Line 1 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 25 minutes
- Line 2: 65 minutes
- Line 3: 195 minutes

2. Identify bottleneck: The line with maximum load = Line 3
3. Bottleneck load: 195 minutes

Answer: Line 3 (195 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.

Question 3

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 2 - Assemble: 45 min on Line 1 - Package: 15 min on Line 1 **Product Y:** - Cut: 20 min on Line 2 - Assemble: 60 min on Line 2 - Package: 20 min on Line 2 **Product Z:** - Cut: 40 min on Line 1 - Assemble: 30 min on Line 3 - Package: 25 min on Line 3 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 100 minutes
- Line 2: 130 minutes
- Line 3: 55 minutes

2. Identify bottleneck: The line with maximum load = Line 2
3. Bottleneck load: 130 minutes

Answer: Line 2 (130 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.

Question 4

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 3 - Assemble: 45 min on Line 1 - Package: 15 min on Line 3 **Product Y:** - Cut: 20 min on Line 2 - Assemble: 60 min on Line 1 - Package: 20 min on Line 2 **Product Z:** - Cut: 40 min on Line 3 - Assemble: 30 min on Line 1 - Package: 25 min on Line 3 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 135 minutes
- Line 2: 40 minutes
- Line 3: 110 minutes

2. Identify bottleneck: The line with maximum load = Line 1
3. Bottleneck load: 135 minutes

Answer: Line 1 (135 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.

Question 5

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 1 - Assemble: 45 min on Line 1 - Package: 15 min on Line 1 **Product Y:** - Cut: 20 min on Line 2 - Assemble: 60 min on Line 1 - Package: 20 min on Line 1 **Product Z:** - Cut: 40 min on Line 3 - Assemble: 30 min on Line 3 - Package: 25 min on Line 1 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 195 minutes
- Line 2: 20 minutes
- Line 3: 70 minutes

2. Identify bottleneck: The line with maximum load = Line 1
3. Bottleneck load: 195 minutes

Answer: Line 1 (195 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.

Question 6

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 1 - Assemble: 45 min on Line 2 - Package: 15 min on Line 2 **Product Y:** - Cut: 20 min on Line 1 - Assemble: 60 min on Line 2 - Package: 20 min on Line 3 **Product Z:** - Cut: 40 min on Line 1 - Assemble: 30 min on Line 1 - Package: 25 min on Line 1 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 145 minutes
- Line 2: 120 minutes
- Line 3: 20 minutes

2. Identify bottleneck: The line with maximum load = Line 1
3. Bottleneck load: 145 minutes

Answer: Line 1 (145 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.

Question 7

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 2 - Assemble: 45 min on Line 1 - Package: 15 min on Line 3 **Product Y:** - Cut: 20 min on Line 3 - Assemble: 60 min on Line 1 - Package: 20 min on Line 2 **Product Z:** - Cut: 40 min on Line 1 - Assemble: 30 min on Line 3 - Package: 25 min on Line 2 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 145 minutes
- Line 2: 75 minutes
- Line 3: 65 minutes

2. Identify bottleneck: The line with maximum load = Line 1
3. Bottleneck load: 145 minutes

Answer: Line 1 (145 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.

Question 8

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 1 - Assemble: 45 min on Line 1 - Package: 15 min on Line 2 **Product Y:** - Cut: 20 min on Line 1 - Assemble: 60 min on Line 2 - Package: 20 min on Line 3 **Product Z:** - Cut: 40 min on Line 2 - Assemble: 30 min on Line 1 - Package: 25 min on Line 2 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 125 minutes
- Line 2: 140 minutes
- Line 3: 20 minutes

2. Identify bottleneck: The line with maximum load = Line 2
3. Bottleneck load: 140 minutes

Answer: Line 2 (140 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.

Question 9

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 1 - Assemble: 45 min on Line 1 - Package: 15 min on Line 1 **Product Y:** - Cut: 20 min on Line 3 - Assemble: 60 min on Line 1 - Package: 20 min on Line 1 **Product Z:** - Cut: 40 min on Line 3 - Assemble: 30 min on Line 1 - Package: 25 min on Line 2 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 200 minutes
- Line 2: 25 minutes
- Line 3: 60 minutes

2. Identify bottleneck: The line with maximum load = Line 1
3. Bottleneck load: 200 minutes

Answer: Line 1 (200 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.

Question 10

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 3 - Assemble: 45 min on Line 2 - Package: 15 min on Line 3 **Product Y:** - Cut: 20 min on Line 1 - Assemble: 60 min on Line 3 - Package: 20 min on Line 2 **Product Z:** - Cut: 40 min on Line 1 - Assemble: 30 min on Line 2 - Package: 25 min on Line 1 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 85 minutes
- Line 2: 95 minutes
- Line 3: 105 minutes

2. Identify bottleneck: The line with maximum load = Line 3
3. Bottleneck load: 105 minutes

Answer: Line 3 (105 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.

Question 11

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 3 - Assemble: 45 min on Line 2 - Package: 15 min on Line 1 **Product Y:** - Cut: 20 min on Line 3 - Assemble: 60 min on Line 3 - Package: 20 min on Line 2 **Product Z:** - Cut: 40 min on Line 3 - Assemble: 30 min on Line 3 - Package: 25 min on Line 3 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 15 minutes
- Line 2: 65 minutes
- Line 3: 205 minutes

2. Identify bottleneck: The line with maximum load = Line 3
3. Bottleneck load: 205 minutes

Answer: Line 3 (205 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.

Question 12

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 1 - Assemble: 45 min on Line 3 - Package: 15 min on Line 3 **Product Y:** - Cut: 20 min on Line 2 - Assemble: 60 min on Line 2 - Package: 20 min on Line 3 **Product Z:** - Cut: 40 min on Line 3 - Assemble: 30 min on Line 2 - Package: 25 min on Line 2 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 30 minutes
- Line 2: 135 minutes
- Line 3: 120 minutes

2. Identify bottleneck: The line with maximum load = Line 2
3. Bottleneck load: 135 minutes

Answer: Line 2 (135 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.

Question 13

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 3 - Assemble: 45 min on Line 3 - Package: 15 min on Line 3 **Product Y:** - Cut: 20 min on Line 1 - Assemble: 60 min on Line 2 - Package: 20 min on Line 3 **Product Z:** - Cut: 40 min on Line 2 - Assemble: 30 min on Line 1 - Package: 25 min on Line 1 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 75 minutes
- Line 2: 100 minutes
- Line 3: 110 minutes

2. Identify bottleneck: The line with maximum load = Line 3
3. Bottleneck load: 110 minutes

Answer: Line 3 (110 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.

Question 14

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 3 - Assemble: 45 min on Line 3 - Package: 15 min on Line 3 **Product Y:** - Cut: 20 min on Line 1 - Assemble: 60 min on Line 3 - Package: 20 min on Line 1 **Product Z:** - Cut: 40 min on Line 2 - Assemble: 30 min on Line 1 - Package: 25 min on Line 2 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 70 minutes
- Line 2: 65 minutes
- Line 3: 150 minutes

2. Identify bottleneck: The line with maximum load = Line 3
3. Bottleneck load: 150 minutes

Answer: Line 3 (150 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.

Question 15

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 1 - Assemble: 45 min on Line 1 - Package: 15 min on Line 1 **Product Y:** - Cut: 20 min on Line 2 - Assemble: 60 min on Line 3 - Package: 20 min on Line 3 **Product Z:** - Cut: 40 min on Line 3 - Assemble: 30 min on Line 2 - Package: 25 min on Line 3 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 90 minutes
- Line 2: 50 minutes
- Line 3: 145 minutes

2. Identify bottleneck: The line with maximum load = Line 3
3. Bottleneck load: 145 minutes

Answer: Line 3 (145 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.

Question 16

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 3 - Assemble: 45 min on Line 3 - Package: 15 min on Line 1 **Product Y:** - Cut: 20 min on Line 2 - Assemble: 60 min on Line 1 - Package: 20 min on Line 2 **Product Z:** - Cut: 40 min on Line 1 - Assemble: 30 min on Line 2 - Package: 25 min on Line 3 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 115 minutes
- Line 2: 70 minutes
- Line 3: 100 minutes

2. Identify bottleneck: The line with maximum load = Line 1
3. Bottleneck load: 115 minutes

Answer: Line 1 (115 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.

Question 17

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 3 - Assemble: 45 min on Line 1 - Package: 15 min on Line 2 **Product Y:** - Cut: 20 min on Line 3 - Assemble: 60 min on Line 3 - Package: 20 min on Line 1 **Product Z:** - Cut: 40 min on Line 2 - Assemble: 30 min on Line 2 - Package: 25 min on Line 2 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 65 minutes
- Line 2: 110 minutes
- Line 3: 110 minutes

2. Identify bottleneck: The line with maximum load = Line 2
3. Bottleneck load: 110 minutes

Answer: Line 2 (110 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.

Question 18

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 1 - Assemble: 45 min on Line 3 - Package: 15 min on Line 2 **Product Y:** - Cut: 20 min on Line 3 - Assemble: 60 min on Line 2 - Package: 20 min on Line 3 **Product Z:** - Cut: 40 min on Line 1 - Assemble: 30 min on Line 2 - Package: 25 min on Line 2 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 70 minutes
- Line 2: 130 minutes
- Line 3: 85 minutes

2. Identify bottleneck: The line with maximum load = Line 2
3. Bottleneck load: 130 minutes

Answer: Line 2 (130 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.

Question 19

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 3 - Assemble: 45 min on Line 2 - Package: 15 min on Line 3 **Product Y:** - Cut: 20 min on Line 3 - Assemble: 60 min on Line 2 - Package: 20 min on Line 2 **Product Z:** - Cut: 40 min on Line 1 - Assemble: 30 min on Line 3 - Package: 25 min on Line 1 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 65 minutes
- Line 2: 125 minutes
- Line 3: 95 minutes

2. Identify bottleneck: The line with maximum load = Line 2
3. Bottleneck load: 125 minutes

Answer: Line 2 (125 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.

Question 20

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 1 - Assemble: 45 min on Line 1 - Package: 15 min on Line 2 **Product Y:** - Cut: 20 min on Line 3 - Assemble: 60 min on Line 1 - Package: 20 min on Line 2 **Product Z:** - Cut: 40 min on Line 2 - Assemble: 30 min on Line 2 - Package: 25 min on Line 3 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 135 minutes
- Line 2: 105 minutes
- Line 3: 45 minutes

2. Identify bottleneck: The line with maximum load = Line 1
3. Bottleneck load: 135 minutes

Answer: Line 1 (135 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.
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