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Master Learning Curve Scheduling - Beginner Level Problems Learning Curve Scheduling BEGINNER

Excel in competitive exams with this skill builder ⚡ worksheet on Learning Curve Scheduling. Worksheet 3 of 10 contains 20 beginner-level problems. Target your step-by-step problem solving skills while practicing learning curve scheduling practice, learning curve scheduling for competitive exams, and how to solve learning curve scheduling.

📝 Worksheet 3 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner level

What you'll learn in this worksheet:
Your progress through Learning Curve Scheduling
Worksheet 3 of 10 (22% complete)

Question 1

A factory produces Widgets with a 90% learning curve (each doubling of cumulative production reduces time by 9%). First unit takes 91 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^-0.152
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): 64.0 minutes
Batch 2 (40 units): 50.5 minutes
Batch 3 (10 units): 47.2 minutes

4. Total time: 161.7 ≈ 162 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 112 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): 63.0 minutes
Batch 2 (10 units): 39.9 minutes
Batch 3 (30 units): 33.2 minutes

4. Total time: 136.0 ≈ 136 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 100 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): 70.3 minutes
Batch 2 (20 units): 38.9 minutes
Batch 3 (30 units): 29.6 minutes

4. Total time: 138.8 ≈ 139 minutes

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

Question 4

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): 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): 40.8 minutes
Batch 2 (40 units): 26.9 minutes
Batch 3 (10 units): 23.7 minutes

4. Total time: 91.3 ≈ 91 minutes

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

Question 5

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 6

A factory produces Widgets with a 90% learning curve (each doubling of cumulative production reduces time by 9%). First unit takes 82 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): 61.3 minutes
Batch 2 (10 units): 50.3 minutes
Batch 3 (40 units): 45.5 minutes

4. Total time: 157.1 ≈ 157 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 66 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^-0.234
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): 36.3 minutes
Batch 2 (10 units): 27.1 minutes
Batch 3 (20 units): 25.3 minutes

4. Total time: 88.7 ≈ 89 minutes

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

Question 8

A factory produces Widgets with a 85% learning curve (each doubling of cumulative production reduces time by 15%). First unit takes 77 minutes. Batch sizes (in order): 30, 20, 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): 45.3 minutes
Batch 2 (20 units): 32.5 minutes
Batch 3 (10 units): 30.1 minutes

4. Total time: 107.9 ≈ 108 minutes

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

Question 9

A factory produces Widgets with a 85% learning curve (each doubling of cumulative production reduces time by 15%). First unit takes 89 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^-0.234
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): 57.6 minutes
Batch 2 (30 units): 39.0 minutes
Batch 3 (40 units): 33.0 minutes

4. Total time: 129.6 ≈ 130 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 103 minutes. Batch sizes (in order): 10, 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^-0.234
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): 78.4 minutes
Batch 2 (40 units): 47.6 minutes
Batch 3 (30 units): 38.8 minutes

4. Total time: 164.8 ≈ 165 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 120 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): 66.0 minutes
Batch 2 (30 units): 47.1 minutes
Batch 3 (10 units): 43.6 minutes

4. Total time: 156.7 ≈ 157 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 66 minutes. Batch sizes (in order): 40, 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 (40 units): 36.3 minutes
Batch 2 (20 units): 26.4 minutes
Batch 3 (30 units): 24.0 minutes

4. Total time: 86.8 ≈ 87 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 78 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^-0.152
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): 64.8 minutes
Batch 2 (20 units): 49.9 minutes
Batch 3 (40 units): 43.3 minutes

4. Total time: 157.9 ≈ 158 minutes

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

Question 14

A factory produces Widgets with a 90% learning curve (each doubling of cumulative production reduces time by 9%). First unit takes 74 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): 61.5 minutes
Batch 2 (40 units): 44.8 minutes
Batch 3 (20 units): 39.7 minutes

4. Total time: 146.1 ≈ 146 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 95 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): 71.1 minutes
Batch 2 (40 units): 54.7 minutes
Batch 3 (30 units): 49.3 minutes

4. Total time: 175.1 ≈ 175 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 87 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): 48.9 minutes
Batch 2 (10 units): 31.0 minutes
Batch 3 (30 units): 25.8 minutes

4. Total time: 105.6 ≈ 106 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 84 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^-0.322
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): 41.4 minutes
Batch 2 (10 units): 26.8 minutes
Batch 3 (40 units): 22.7 minutes

4. Total time: 90.9 ≈ 91 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 62 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): 40.1 minutes
Batch 2 (40 units): 26.5 minutes
Batch 3 (10 units): 23.3 minutes

4. Total time: 89.9 ≈ 90 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 67 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^-0.322
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): 47.1 minutes
Batch 2 (20 units): 26.0 minutes
Batch 3 (40 units): 19.2 minutes

4. Total time: 92.4 ≈ 92 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 80 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): 39.5 minutes
Batch 2 (40 units): 23.0 minutes
Batch 3 (10 units): 19.9 minutes

4. Total time: 82.4 ≈ 82 minutes

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