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Learning Curve Scheduling Beginner-Intermediate Worksheet: Focus on common variations practice Learning Curve Scheduling BEGINNER INTERMEDIATE

Level up your Learning Curve Scheduling 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: learning curve scheduling for competitive exams, how to solve learning curve scheduling, learning curve scheduling tricks.

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

What you'll learn in this worksheet:
Your progress through Learning Curve Scheduling
Worksheet 4 of 10 (33% complete)

Question 1

A factory produces Widgets with a 85% learning curve (each doubling of cumulative production reduces time by 15%). First unit takes 102 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): 66.0 minutes
Batch 2 (10 units): 48.0 minutes
Batch 3 (40 units): 41.1 minutes

4. Total time: 155.2 ≈ 155 minutes

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

Question 2

A factory produces Widgets with a 85% learning curve (each doubling of cumulative production reduces time by 15%). First unit takes 61 minutes. Batch sizes (in order): 30, 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 (30 units): 35.9 minutes
Batch 2 (40 units): 24.6 minutes
Batch 3 (20 units): 21.8 minutes

4. Total time: 82.3 ≈ 82 minutes

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

Question 3

A factory produces Widgets with a 80% learning curve (each doubling of cumulative production reduces time by 19%). First unit takes 115 minutes. Batch sizes (in order): 20, 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^-0.322
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): 64.7 minutes
Batch 2 (30 units): 37.1 minutes
Batch 3 (40 units): 29.5 minutes

4. Total time: 131.2 ≈ 131 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 87 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^-0.322
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): 61.1 minutes
Batch 2 (40 units): 30.2 minutes
Batch 3 (20 units): 23.3 minutes

4. Total time: 114.7 ≈ 115 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 66 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^-0.152
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): 54.8 minutes
Batch 2 (20 units): 42.2 minutes
Batch 3 (30 units): 37.1 minutes

4. Total time: 134.2 ≈ 134 minutes

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

Question 6

A factory produces Widgets with a 90% learning curve (each doubling of cumulative production reduces time by 9%). First unit takes 100 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^-0.152
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): 83.1 minutes
Batch 2 (30 units): 62.0 minutes
Batch 3 (20 units): 55.2 minutes

4. Total time: 200.4 ≈ 200 minutes

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

Question 7

A factory produces Widgets with a 90% learning curve (each doubling of cumulative production reduces time by 9%). First unit takes 98 minutes. Batch sizes (in order): 30, 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 (30 units): 68.9 minutes
Batch 2 (40 units): 54.3 minutes
Batch 3 (20 units): 50.4 minutes

4. Total time: 173.6 ≈ 174 minutes

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

Question 8

A factory produces Widgets with a 80% learning curve (each doubling of cumulative production reduces time by 19%). First unit takes 103 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^-0.322
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): 57.9 minutes
Batch 2 (40 units): 32.0 minutes
Batch 3 (10 units): 26.9 minutes

4. Total time: 116.8 ≈ 117 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 107 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^-0.152
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): 80.0 minutes
Batch 2 (10 units): 65.7 minutes
Batch 3 (40 units): 59.3 minutes

4. Total time: 205.0 ≈ 205 minutes

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

Question 10

A factory produces Widgets with a 90% learning curve (each doubling of cumulative production reduces time by 9%). First unit takes 88 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): 73.1 minutes
Batch 2 (40 units): 53.3 minutes
Batch 3 (20 units): 47.3 minutes

4. Total time: 173.7 ≈ 174 minutes

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

Question 11

A factory produces Widgets with a 80% learning curve (each doubling of cumulative production reduces time by 19%). First unit takes 76 minutes. Batch sizes (in order): 20, 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 (20 units): 42.7 minutes
Batch 2 (10 units): 27.0 minutes
Batch 3 (30 units): 22.5 minutes

4. Total time: 92.3 ≈ 92 minutes

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

Question 12

A factory produces Widgets with a 90% learning curve (each doubling of cumulative production reduces time by 9%). First unit takes 88 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^-0.152
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 (40 units): 59.2 minutes
Batch 2 (10 units): 49.4 minutes
Batch 3 (20 units): 47.3 minutes

4. Total time: 155.9 ≈ 156 minutes

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

Question 13

A factory produces Widgets with a 90% learning curve (each doubling of cumulative production reduces time by 9%). First unit takes 88 minutes. Batch sizes (in order): 20, 40, 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^-0.152
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): 65.8 minutes
Batch 2 (40 units): 50.6 minutes
Batch 3 (30 units): 45.7 minutes

4. Total time: 162.2 ≈ 162 minutes

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

Question 14

A factory produces Widgets with a 85% learning curve (each doubling of cumulative production reduces time by 15%). First unit takes 84 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): 46.2 minutes
Batch 2 (30 units): 32.9 minutes
Batch 3 (10 units): 30.5 minutes

4. Total time: 109.7 ≈ 110 minutes

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

Question 15

A factory produces Widgets with a 80% learning curve (each doubling of cumulative production reduces time by 19%). First unit takes 71 minutes. Batch sizes (in order): 40, 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 (40 units): 31.9 minutes
Batch 2 (30 units): 19.6 minutes
Batch 3 (20 units): 17.3 minutes

4. Total time: 68.9 ≈ 69 minutes

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

Question 16

A factory produces Widgets with a 85% learning curve (each doubling of cumulative production reduces time by 15%). First unit takes 66 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^-0.234
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): 50.2 minutes
Batch 2 (30 units): 31.7 minutes
Batch 3 (40 units): 25.4 minutes

4. Total time: 107.3 ≈ 107 minutes

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

Question 17

A factory produces Widgets with a 90% learning curve (each doubling of cumulative production reduces time by 9%). First unit takes 97 minutes. Batch sizes (in order): 30, 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^-0.152
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): 68.2 minutes
Batch 2 (10 units): 56.5 minutes
Batch 3 (40 units): 52.2 minutes

4. Total time: 177.0 ≈ 177 minutes

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

Question 18

A factory produces Widgets with a 85% learning curve (each doubling of cumulative production reduces time by 15%). First unit takes 95 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^-0.234
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): 61.5 minutes
Batch 2 (40 units): 40.5 minutes
Batch 3 (10 units): 35.7 minutes

4. Total time: 137.7 ≈ 138 minutes

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

Question 19

A factory produces Widgets with a 85% learning curve (each doubling of cumulative production reduces time by 15%). First unit takes 64 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): 48.7 minutes
Batch 2 (20 units): 32.1 minutes
Batch 3 (30 units): 26.4 minutes

4. Total time: 107.2 ≈ 107 minutes

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

Question 20

A factory produces Widgets with a 80% learning curve (each doubling of cumulative production reduces time by 19%). First unit takes 60 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): 33.7 minutes
Batch 2 (30 units): 19.4 minutes
Batch 3 (10 units): 16.5 minutes

4. Total time: 69.6 ≈ 70 minutes

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