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Learning Curve Scheduling - Intermediate Level: tricky scenarios handling Learning Curve Scheduling INTERMEDIATE

This expert challenge 📈 worksheet focuses on Learning Curve Scheduling - a key topic in Scheduling. You'll solve 20 intermediate-level problems (Worksheet 5 of 10). The primary focus is on tricky scenarios handling. Master how to solve learning curve scheduling, learning curve scheduling tricks, and learning curve scheduling shortcut methods through systematic practice.

📝 Worksheet 5 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Learning Curve Scheduling
Worksheet 5 of 10 (44% complete)

Question 1

A factory produces Widgets with a 80% learning curve (each doubling of cumulative production reduces time by 19%). First unit takes 85 minutes. Batch sizes (in order): 30, 10, 20 units. What is the TOTAL production time for all batches (in minutes, rounded to nearest minute)?
Step-by-step solution (Learning Curve):

1. Learning curve formula: T_n = T_1 × n^-0.322
where exponent = log(0.8)/log(2) = -0.322

2. Calculate cumulative time using integration:
Cumulative time for N units = T_1 × N^0.6780719051126377 / (learning_exponent + 1)

3. Time per batch:
Batch 1 (30 units): 41.9 minutes
Batch 2 (10 units): 27.1 minutes
Batch 3 (20 units): 24.2 minutes

4. Total time: 93.2 ≈ 93 minutes

Key Strategy: Learning curve reduces time with repetition; use cumulative average method for batch calculations.

Question 2

A factory produces Widgets with a 80% learning curve (each doubling of cumulative production reduces time by 19%). First unit takes 94 minutes. Batch sizes (in order): 10, 20, 30 units. What is the TOTAL production time for all batches (in minutes, rounded to nearest minute)?
Step-by-step solution (Learning Curve):

1. Learning curve formula: T_n = T_1 × n^-0.322
where exponent = log(0.8)/log(2) = -0.322

2. Calculate cumulative time using integration:
Cumulative time for N units = T_1 × N^0.6780719051126377 / (learning_exponent + 1)

3. Time per batch:
Batch 1 (10 units): 66.1 minutes
Batch 2 (20 units): 36.5 minutes
Batch 3 (30 units): 27.8 minutes

4. Total time: 130.4 ≈ 130 minutes

Key Strategy: Learning curve reduces time with repetition; use cumulative average method for batch calculations.

Question 3

A factory produces Widgets with a 85% learning curve (each doubling of cumulative production reduces time by 15%). First unit takes 94 minutes. Batch sizes (in order): 20, 10, 40 units. What is the TOTAL production time for all batches (in minutes, rounded to nearest minute)?
Step-by-step solution (Learning Curve):

1. Learning curve formula: T_n = T_1 × n^-0.234
where exponent = log(0.85)/log(2) = -0.234

2. Calculate cumulative time using integration:
Cumulative time for N units = T_1 × N^0.765534746362977 / (learning_exponent + 1)

3. Time per batch:
Batch 1 (20 units): 60.8 minutes
Batch 2 (10 units): 44.3 minutes
Batch 3 (40 units): 37.9 minutes

4. Total time: 143.0 ≈ 143 minutes

Key Strategy: Learning curve reduces time with repetition; use cumulative average method for batch calculations.

Question 4

A factory produces Widgets with a 80% learning curve (each doubling of cumulative production reduces time by 19%). First unit takes 104 minutes. Batch sizes (in order): 30, 40, 10 units. What is the TOTAL production time for all batches (in minutes, rounded to nearest minute)?
Step-by-step solution (Learning Curve):

1. Learning curve formula: T_n = T_1 × n^-0.322
where exponent = log(0.8)/log(2) = -0.322

2. Calculate cumulative time using integration:
Cumulative time for N units = T_1 × N^0.6780719051126377 / (learning_exponent + 1)

3. Time per batch:
Batch 1 (30 units): 51.3 minutes
Batch 2 (40 units): 29.9 minutes
Batch 3 (10 units): 25.9 minutes

4. Total time: 107.1 ≈ 107 minutes

Key Strategy: Learning curve reduces time with repetition; use cumulative average method for batch calculations.

Question 5

A factory produces Widgets with a 90% learning curve (each doubling of cumulative production reduces time by 9%). First unit takes 64 minutes. Batch sizes (in order): 10, 40, 20 units. What is the TOTAL production time for all batches (in minutes, rounded to nearest minute)?
Step-by-step solution (Learning Curve):

1. Learning curve formula: T_n = T_1 × n^-0.152
where exponent = log(0.9)/log(2) = -0.152

2. Calculate cumulative time using integration:
Cumulative time for N units = T_1 × N^0.84799690655495 / (learning_exponent + 1)

3. Time per batch:
Batch 1 (10 units): 53.2 minutes
Batch 2 (40 units): 38.8 minutes
Batch 3 (20 units): 34.4 minutes

4. Total time: 126.3 ≈ 126 minutes

Key Strategy: Learning curve reduces time with repetition; use cumulative average method for batch calculations.

Question 6

A factory produces Widgets with a 85% learning curve (each doubling of cumulative production reduces time by 15%). First unit takes 69 minutes. Batch sizes (in order): 30, 20, 40 units. What is the TOTAL production time for all batches (in minutes, rounded to nearest minute)?
Step-by-step solution (Learning Curve):

1. Learning curve formula: T_n = T_1 × n^-0.234
where exponent = log(0.85)/log(2) = -0.234

2. Calculate cumulative time using integration:
Cumulative time for N units = T_1 × N^0.765534746362977 / (learning_exponent + 1)

3. Time per batch:
Batch 1 (30 units): 40.6 minutes
Batch 2 (20 units): 29.1 minutes
Batch 3 (40 units): 25.6 minutes

4. Total time: 95.3 ≈ 95 minutes

Key Strategy: Learning curve reduces time with repetition; use cumulative average method for batch calculations.

Question 7

A factory produces Widgets with a 85% learning curve (each doubling of cumulative production reduces time by 15%). First unit takes 60 minutes. Batch sizes (in order): 40, 10, 30 units. What is the TOTAL production time for all batches (in minutes, rounded to nearest minute)?
Step-by-step solution (Learning Curve):

1. Learning curve formula: T_n = T_1 × n^-0.234
where exponent = log(0.85)/log(2) = -0.234

2. Calculate cumulative time using integration:
Cumulative time for N units = T_1 × N^0.765534746362977 / (learning_exponent + 1)

3. Time per batch:
Batch 1 (40 units): 33.0 minutes
Batch 2 (10 units): 24.6 minutes
Batch 3 (30 units): 22.6 minutes

4. Total time: 80.2 ≈ 80 minutes

Key Strategy: Learning curve reduces time with repetition; use cumulative average method for batch calculations.

Question 8

A factory produces Widgets with a 90% learning curve (each doubling of cumulative production reduces time by 9%). First unit takes 86 minutes. Batch sizes (in order): 30, 20, 40 units. What is the TOTAL production time for all batches (in minutes, rounded to nearest minute)?
Step-by-step solution (Learning Curve):

1. Learning curve formula: T_n = T_1 × n^-0.152
where exponent = log(0.9)/log(2) = -0.152

2. Calculate cumulative time using integration:
Cumulative time for N units = T_1 × N^0.84799690655495 / (learning_exponent + 1)

3. Time per batch:
Batch 1 (30 units): 60.5 minutes
Batch 2 (20 units): 49.2 minutes
Batch 3 (40 units): 45.2 minutes

4. Total time: 154.9 ≈ 155 minutes

Key Strategy: Learning curve reduces time with repetition; use cumulative average method for batch calculations.

Question 9

A factory produces Widgets with a 90% learning curve (each doubling of cumulative production reduces time by 9%). First unit takes 69 minutes. Batch sizes (in order): 20, 40, 10 units. What is the TOTAL production time for all batches (in minutes, rounded to nearest minute)?
Step-by-step solution (Learning Curve):

1. Learning curve formula: T_n = T_1 × n^-0.152
where exponent = log(0.9)/log(2) = -0.152

2. Calculate cumulative time using integration:
Cumulative time for N units = T_1 × N^0.84799690655495 / (learning_exponent + 1)

3. Time per batch:
Batch 1 (20 units): 51.6 minutes
Batch 2 (40 units): 39.7 minutes
Batch 3 (10 units): 36.6 minutes

4. Total time: 127.9 ≈ 128 minutes

Key Strategy: Learning curve reduces time with repetition; use cumulative average method for batch calculations.

Question 10

A factory produces Widgets with a 85% learning curve (each doubling of cumulative production reduces time by 15%). First unit takes 88 minutes. Batch sizes (in order): 30, 40, 10 units. What is the TOTAL production time for all batches (in minutes, rounded to nearest minute)?
Step-by-step solution (Learning Curve):

1. Learning curve formula: T_n = T_1 × n^-0.234
where exponent = log(0.85)/log(2) = -0.234

2. Calculate cumulative time using integration:
Cumulative time for N units = T_1 × N^0.765534746362977 / (learning_exponent + 1)

3. Time per batch:
Batch 1 (30 units): 51.8 minutes
Batch 2 (40 units): 35.5 minutes
Batch 3 (10 units): 32.0 minutes

4. Total time: 119.2 ≈ 119 minutes

Key Strategy: Learning curve reduces time with repetition; use cumulative average method for batch calculations.

Question 11

A factory produces Widgets with a 85% learning curve (each doubling of cumulative production reduces time by 15%). First unit takes 63 minutes. Batch sizes (in order): 40, 30, 10 units. What is the TOTAL production time for all batches (in minutes, rounded to nearest minute)?
Step-by-step solution (Learning Curve):

1. Learning curve formula: T_n = T_1 × n^-0.234
where exponent = log(0.85)/log(2) = -0.234

2. Calculate cumulative time using integration:
Cumulative time for N units = T_1 × N^0.765534746362977 / (learning_exponent + 1)

3. Time per batch:
Batch 1 (40 units): 34.7 minutes
Batch 2 (30 units): 24.7 minutes
Batch 3 (10 units): 22.9 minutes

4. Total time: 82.3 ≈ 82 minutes

Key Strategy: Learning curve reduces time with repetition; use cumulative average method for batch calculations.

Question 12

A factory produces Widgets with a 85% learning curve (each doubling of cumulative production reduces time by 15%). First unit takes 107 minutes. Batch sizes (in order): 10, 40, 20 units. What is the TOTAL production time for all batches (in minutes, rounded to nearest minute)?
Step-by-step solution (Learning Curve):

1. Learning curve formula: T_n = T_1 × n^-0.234
where exponent = log(0.85)/log(2) = -0.234

2. Calculate cumulative time using integration:
Cumulative time for N units = T_1 × N^0.765534746362977 / (learning_exponent + 1)

3. Time per batch:
Batch 1 (10 units): 81.5 minutes
Batch 2 (40 units): 49.5 minutes
Batch 3 (20 units): 41.0 minutes

4. Total time: 171.9 ≈ 172 minutes

Key Strategy: Learning curve reduces time with repetition; use cumulative average method for batch calculations.

Question 13

A factory produces Widgets with a 85% learning curve (each doubling of cumulative production reduces time by 15%). First unit takes 80 minutes. Batch sizes (in order): 10, 20, 40 units. What is the TOTAL production time for all batches (in minutes, rounded to nearest minute)?
Step-by-step solution (Learning Curve):

1. Learning curve formula: T_n = T_1 × n^-0.234
where exponent = log(0.85)/log(2) = -0.234

2. Calculate cumulative time using integration:
Cumulative time for N units = T_1 × N^0.765534746362977 / (learning_exponent + 1)

3. Time per batch:
Batch 1 (10 units): 60.9 minutes
Batch 2 (20 units): 40.2 minutes
Batch 3 (40 units): 32.2 minutes

4. Total time: 133.3 ≈ 133 minutes

Key Strategy: Learning curve reduces time with repetition; use cumulative average method for batch calculations.

Question 14

A factory produces Widgets with a 80% learning curve (each doubling of cumulative production reduces time by 19%). First unit takes 73 minutes. Batch sizes (in order): 10, 30, 20 units. What is the TOTAL production time for all batches (in minutes, rounded to nearest minute)?
Step-by-step solution (Learning Curve):

1. Learning curve formula: T_n = T_1 × n^-0.322
where exponent = log(0.8)/log(2) = -0.322

2. Calculate cumulative time using integration:
Cumulative time for N units = T_1 × N^0.6780719051126377 / (learning_exponent + 1)

3. Time per batch:
Batch 1 (10 units): 51.3 minutes
Batch 2 (30 units): 26.7 minutes
Batch 3 (20 units): 20.8 minutes

4. Total time: 98.8 ≈ 99 minutes

Key Strategy: Learning curve reduces time with repetition; use cumulative average method for batch calculations.

Question 15

A factory produces Widgets with a 90% learning curve (each doubling of cumulative production reduces time by 9%). First unit takes 80 minutes. Batch sizes (in order): 10, 30, 40 units. What is the TOTAL production time for all batches (in minutes, rounded to nearest minute)?
Step-by-step solution (Learning Curve):

1. Learning curve formula: T_n = T_1 × n^-0.152
where exponent = log(0.9)/log(2) = -0.152

2. Calculate cumulative time using integration:
Cumulative time for N units = T_1 × N^0.84799690655495 / (learning_exponent + 1)

3. Time per batch:
Batch 1 (10 units): 66.5 minutes
Batch 2 (30 units): 49.6 minutes
Batch 3 (40 units): 43.1 minutes

4. Total time: 159.2 ≈ 159 minutes

Key Strategy: Learning curve reduces time with repetition; use cumulative average method for batch calculations.

Question 16

A factory produces Widgets with a 80% learning curve (each doubling of cumulative production reduces time by 19%). First unit takes 95 minutes. Batch sizes (in order): 20, 30, 10 units. What is the TOTAL production time for all batches (in minutes, rounded to nearest minute)?
Step-by-step solution (Learning Curve):

1. Learning curve formula: T_n = T_1 × n^-0.322
where exponent = log(0.8)/log(2) = -0.322

2. Calculate cumulative time using integration:
Cumulative time for N units = T_1 × N^0.6780719051126377 / (learning_exponent + 1)

3. Time per batch:
Batch 1 (20 units): 53.4 minutes
Batch 2 (30 units): 30.7 minutes
Batch 3 (10 units): 26.2 minutes

4. Total time: 110.2 ≈ 110 minutes

Key Strategy: Learning curve reduces time with repetition; use cumulative average method for batch calculations.

Question 17

A factory produces Widgets with a 80% learning curve (each doubling of cumulative production reduces time by 19%). First unit takes 65 minutes. Batch sizes (in order): 40, 10, 30 units. What is the TOTAL production time for all batches (in minutes, rounded to nearest minute)?
Step-by-step solution (Learning Curve):

1. Learning curve formula: T_n = T_1 × n^-0.322
where exponent = log(0.8)/log(2) = -0.322

2. Calculate cumulative time using integration:
Cumulative time for N units = T_1 × N^0.6780719051126377 / (learning_exponent + 1)

3. Time per batch:
Batch 1 (40 units): 29.2 minutes
Batch 2 (10 units): 19.1 minutes
Batch 3 (30 units): 17.0 minutes

4. Total time: 65.4 ≈ 65 minutes

Key Strategy: Learning curve reduces time with repetition; use cumulative average method for batch calculations.

Question 18

A factory produces Widgets with a 80% learning curve (each doubling of cumulative production reduces time by 19%). First unit takes 112 minutes. Batch sizes (in order): 40, 10, 20 units. What is the TOTAL production time for all batches (in minutes, rounded to nearest minute)?
Step-by-step solution (Learning Curve):

1. Learning curve formula: T_n = T_1 × n^-0.322
where exponent = log(0.8)/log(2) = -0.322

2. Calculate cumulative time using integration:
Cumulative time for N units = T_1 × N^0.6780719051126377 / (learning_exponent + 1)

3. Time per batch:
Batch 1 (40 units): 50.4 minutes
Batch 2 (10 units): 32.9 minutes
Batch 3 (20 units): 30.0 minutes

4. Total time: 113.3 ≈ 113 minutes

Key Strategy: Learning curve reduces time with repetition; use cumulative average method for batch calculations.

Question 19

A factory produces Widgets with a 80% learning curve (each doubling of cumulative production reduces time by 19%). First unit takes 112 minutes. Batch sizes (in order): 10, 30, 20 units. What is the TOTAL production time for all batches (in minutes, rounded to nearest minute)?
Step-by-step solution (Learning Curve):

1. Learning curve formula: T_n = T_1 × n^-0.322
where exponent = log(0.8)/log(2) = -0.322

2. Calculate cumulative time using integration:
Cumulative time for N units = T_1 × N^0.6780719051126377 / (learning_exponent + 1)

3. Time per batch:
Batch 1 (10 units): 78.7 minutes
Batch 2 (30 units): 40.9 minutes
Batch 3 (20 units): 31.9 minutes

4. Total time: 151.5 ≈ 152 minutes

Key Strategy: Learning curve reduces time with repetition; use cumulative average method for batch calculations.

Question 20

A factory produces Widgets with a 85% learning curve (each doubling of cumulative production reduces time by 15%). First unit takes 67 minutes. Batch sizes (in order): 10, 20, 30 units. What is the TOTAL production time for all batches (in minutes, rounded to nearest minute)?
Step-by-step solution (Learning Curve):

1. Learning curve formula: T_n = T_1 × n^-0.234
where exponent = log(0.85)/log(2) = -0.234

2. Calculate cumulative time using integration:
Cumulative time for N units = T_1 × N^0.765534746362977 / (learning_exponent + 1)

3. Time per batch:
Batch 1 (10 units): 51.0 minutes
Batch 2 (20 units): 33.6 minutes
Batch 3 (30 units): 27.6 minutes

4. Total time: 112.2 ≈ 112 minutes

Key Strategy: Learning curve reduces time with repetition; use cumulative average method for batch calculations.
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