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Learning Curve Scheduling - Expert Level: conceptual clarity Learning Curve Scheduling EXPERT

This skill evaluation ⚡ worksheet focuses on Learning Curve Scheduling - a key topic in Scheduling. You'll solve 20 expert-level problems (Worksheet 9 of 10). The primary focus is on conceptual clarity. Master learning curve scheduling ssc cgl, learning curve scheduling reasoning tricks, and fast learning curve scheduling solving through systematic practice.

📝 Worksheet 9 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Expert level

What you'll learn in this worksheet:
Your progress through Learning Curve Scheduling
Worksheet 9 of 10 (88% complete)

Question 1

A factory produces Widgets with a 90% learning curve (each doubling of cumulative production reduces time by 9%). First unit takes 111 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): 92.2 minutes
Batch 2 (30 units): 68.9 minutes
Batch 3 (20 units): 61.3 minutes

4. Total time: 222.4 ≈ 222 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 118 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): 53.1 minutes
Batch 2 (30 units): 32.7 minutes
Batch 3 (20 units): 28.8 minutes

4. Total time: 114.5 ≈ 115 minutes

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

Question 3

A factory produces Widgets with a 90% learning curve (each doubling of cumulative production reduces time by 9%). First unit takes 103 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^-0.152
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): 72.4 minutes
Batch 2 (10 units): 60.0 minutes
Batch 3 (20 units): 56.9 minutes

4. Total time: 189.4 ≈ 189 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 77 minutes. Batch sizes (in order): 40, 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 (40 units): 42.4 minutes
Batch 2 (20 units): 30.8 minutes
Batch 3 (10 units): 28.9 minutes

4. Total time: 102.1 ≈ 102 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 68 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): 47.8 minutes
Batch 2 (20 units): 26.4 minutes
Batch 3 (30 units): 20.1 minutes

4. Total time: 94.4 ≈ 94 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 112 minutes. Batch sizes (in order): 40, 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^-0.152
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): 75.4 minutes
Batch 2 (20 units): 61.9 minutes
Batch 3 (10 units): 59.4 minutes

4. Total time: 196.7 ≈ 197 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 69 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): 52.5 minutes
Batch 2 (20 units): 34.6 minutes
Batch 3 (40 units): 27.8 minutes

4. Total time: 115.0 ≈ 115 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 94 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): 42.3 minutes
Batch 2 (10 units): 27.6 minutes
Batch 3 (30 units): 24.6 minutes

4. Total time: 94.5 ≈ 95 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 67 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): 47.1 minutes
Batch 2 (40 units): 37.2 minutes
Batch 3 (20 units): 34.4 minutes

4. Total time: 118.7 ≈ 119 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 104 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): 70.0 minutes
Batch 2 (10 units): 58.3 minutes
Batch 3 (20 units): 55.9 minutes

4. Total time: 184.2 ≈ 184 minutes

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

Question 11

A factory produces Widgets with a 90% learning curve (each doubling of cumulative production reduces time by 9%). First unit takes 110 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): 91.4 minutes
Batch 2 (20 units): 70.3 minutes
Batch 3 (30 units): 61.9 minutes

4. Total time: 223.6 ≈ 224 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): 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): 42.7 minutes
Batch 2 (30 units): 28.9 minutes
Batch 3 (40 units): 24.5 minutes

4. Total time: 96.1 ≈ 96 minutes

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

Question 13

A factory produces Widgets with a 80% learning curve (each doubling of cumulative production reduces time by 19%). 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^-0.322
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): 54.0 minutes
Batch 2 (30 units): 33.2 minutes
Batch 3 (10 units): 29.9 minutes

4. Total time: 117.1 ≈ 117 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 96 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): 71.8 minutes
Batch 2 (40 units): 55.2 minutes
Batch 3 (10 units): 50.9 minutes

4. Total time: 177.9 ≈ 178 minutes

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

Question 15

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): 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): 64.0 minutes
Batch 2 (40 units): 38.8 minutes
Batch 3 (20 units): 32.2 minutes

4. Total time: 135.0 ≈ 135 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 102 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): 66.0 minutes
Batch 2 (30 units): 44.7 minutes
Batch 3 (40 units): 37.8 minutes

4. Total time: 148.6 ≈ 149 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 90 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): 67.3 minutes
Batch 2 (40 units): 51.8 minutes
Batch 3 (30 units): 46.7 minutes

4. Total time: 165.8 ≈ 166 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 85 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): 38.2 minutes
Batch 2 (10 units): 25.0 minutes
Batch 3 (30 units): 22.3 minutes

4. Total time: 85.5 ≈ 85 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 79 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): 60.1 minutes
Batch 2 (40 units): 36.5 minutes
Batch 3 (30 units): 29.8 minutes

4. Total time: 126.4 ≈ 126 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 102 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): 71.7 minutes
Batch 2 (20 units): 39.7 minutes
Batch 3 (30 units): 30.2 minutes

4. Total time: 141.5 ≈ 142 minutes

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