Large-Scale (b) Compute the variance for the profit associated with the two expansion alternatives. Round your answers to whole numbers, if needed. Var Medium-Scale Large-Scale X
Large-Scale (b) Compute the variance for the profit associated with the two expansion alternatives. Round your answers to whole numbers, if needed. Var Medium-Scale Large-Scale X
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 84E
Related questions
Question
100%
![### Decision Analysis for Expansion Alternatives
---
**Demand and Profit Table:**
The table below provides the profits for medium-scale and large-scale expansion alternatives across different levels of demand:
| Demand | Medium-Scale Expansion Profit (`x`) | Probability (`f(x)`) | Large-Scale Expansion Profit (`y`) | Probability (`f(y)`) |
|--------|-------------------------------------|-----------------------|------------------------------------|-----------------------|
| Low | 50 | 0.20 | 0 | 0.20 |
| Medium | 150 | 0.30 | 100 | 0.30 |
| High | 200 | 0.50 | 300 | 0.50 |
---
**Expected Value Calculation (a):**
**Step (a):** Compute the expected value for the profit associated with the two expansion alternatives. Round your answers to whole numbers if needed.
#### Expected Value (EV)
- Medium-Scale Expansion:
\[
EV = (50 \times 0.20) + (150 \times 0.30) + (200 \times 0.50) = 10 + 45 + 100 = 155
\]
- Large-Scale Expansion:
\[
EV = (0 \times 0.20) + (100 \times 0.30) + (300 \times 0.50) = 0 + 30 + 150 = 180
\]
Based on the calculations:
- **Medium-Scale**: 155
- **Large-Scale**: 180
**Preferred Decision:** Large-Scale
The large-scale expansion is preferred for maximizing the expected profit as it has a higher expected value.
---
**Variance Calculation (b):**
**Step (b):** Compute the variance for the profit associated with the two expansion alternatives. Round your answers to whole numbers if needed.
#### Variance (Var)
- Medium-Scale Expansion:
\[
Var = E[X^2] - (E[X])^2
\]
Where \( E[X^2] \) is the expected value of the squared profits,
\[
E[X^2] = (50^2 \times 0.20) + (150^2 \times 0.30) + (200^2 \times 0.50)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff0fc3d30-4939-4166-86b5-591ca635fe70%2F098ba32f-c65e-4674-a8c9-4414444cb46c%2Fbmfq99q_processed.png&w=3840&q=75)
Transcribed Image Text:### Decision Analysis for Expansion Alternatives
---
**Demand and Profit Table:**
The table below provides the profits for medium-scale and large-scale expansion alternatives across different levels of demand:
| Demand | Medium-Scale Expansion Profit (`x`) | Probability (`f(x)`) | Large-Scale Expansion Profit (`y`) | Probability (`f(y)`) |
|--------|-------------------------------------|-----------------------|------------------------------------|-----------------------|
| Low | 50 | 0.20 | 0 | 0.20 |
| Medium | 150 | 0.30 | 100 | 0.30 |
| High | 200 | 0.50 | 300 | 0.50 |
---
**Expected Value Calculation (a):**
**Step (a):** Compute the expected value for the profit associated with the two expansion alternatives. Round your answers to whole numbers if needed.
#### Expected Value (EV)
- Medium-Scale Expansion:
\[
EV = (50 \times 0.20) + (150 \times 0.30) + (200 \times 0.50) = 10 + 45 + 100 = 155
\]
- Large-Scale Expansion:
\[
EV = (0 \times 0.20) + (100 \times 0.30) + (300 \times 0.50) = 0 + 30 + 150 = 180
\]
Based on the calculations:
- **Medium-Scale**: 155
- **Large-Scale**: 180
**Preferred Decision:** Large-Scale
The large-scale expansion is preferred for maximizing the expected profit as it has a higher expected value.
---
**Variance Calculation (b):**
**Step (b):** Compute the variance for the profit associated with the two expansion alternatives. Round your answers to whole numbers if needed.
#### Variance (Var)
- Medium-Scale Expansion:
\[
Var = E[X^2] - (E[X])^2
\]
Where \( E[X^2] \) is the expected value of the squared profits,
\[
E[X^2] = (50^2 \times 0.20) + (150^2 \times 0.30) + (200^2 \times 0.50)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
Similar questions
Recommended textbooks for you
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage