Description
You should work individually. Type your answers in the Answer Sheet part of the assignment. Do not use red color. Use Ariel or Times New Roman 12-point font with 1.5 line spacing
| Course Name | Quantitative Business Analysis | ||
| Course Code | BUS 306 | ||
| Semester | Spring 2020 | ||
| Instructor’s Name | Dr. Djamel Bellout and Dr. Baha Ihnaini | ||
| Questions | 1 | 2 | 3 | 4 | Total |
| Point | 10 | 13 | 10 | 7 | 40 |
| Student Mark |
Note: This Assignment accounts for 40% of the student’s final grade.
Question 1: Problem solving (10 Marks)
The data below is on a variable Y (daily demand on a type of salmon fish in number of units), and a variable X (selling price/unit in AED).
| 51 | 190 | 81 | -468 | |
| 69 | 90 | 81 | -432 | |
| 56 | 140 | 16 | -8 | |
| 64 | 115 | 16 | -92 | |
| 54 | 172 | 36 | -204 | |
| 67 | 85 | 49 | -371 | |
| 59 | 158 | 1 | -20 | |
| 65 | 122 | 25 | -80 | |
| 53 | 198 | 49 | -420 | |
| 62 | 110 | 4 | -56 | |
| Average/Total | = 60 | = 138 | Sum = 358 | Sum = -2151 |
- Based on this scatter diagram, how is the relationship between X and Y ? (1 Mark)
- Use the calculations results in the table above to find the values of b0 and b1, and write the simple regression model to predict Y by X. (3 Marks)
- Using the regression model, find the predicted value of Y if X = 70. (2 Marks)
- If SST = 14546, SSE = 1621.97, and SSR = 12924.03, compute the r2 and write down its interpretation. (2 Marks)
- Write down the hypotheses H0 and H1 for testing the significance of the linear relationship between X and Y, and compute the F-statistic. (2 Marks)
Question 2: Problem solving (13 Marks)
A large-scale tire distribution company wants to determine the best forecast for its month 7 demand. The company’s data on historical monthly demand for the past six months is presented in the following table:
| Month | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Demand (units) | 5,000 | 6,000 | 6,500 | 8,000 | 9,500 | 11,500 | — |
- Compute the demand forecast for month 7 using the simple moving average of order 2, then of order 3. Compute the whole series. (4. Marks)
- Compute the demand forecast for month 7 using the weighted moving average of order 2, with weights from the most recent month as 10 and 5, then of order 3 with weights from the most recent month as 6, 3, and 1. Compute the whole series. (4. Marks)
- Compute the demand forecast for month 7 using the exponential smoothing, assuming that F1= 4,500 units, with α= 0.2 then with α= 0.3. (5 Marks)
Question 3: Problem solving (10 Marks)
Part I: Consider the following Linear Program:
Max Z = 6.x1+ 10.x2
Subject to:
2.x1+ 3.x2 ≤ 36
4.x1+ 2.x2 ≤ 32
x1, x2 ≥ 0
- Represent graphically the feasible region (solution space). (4 Marks)
- Find the Optimal Solution using the graphical method. (4 Marks)
Part II: Answer the following questions:
- Define the special issue of unboundedness, in linear programming problems. (1 Mark)
- Define the special issue of redundancy, in linear programming problems. (1 Mark)
Question 4: Problem solving (7 Marks)
The graph below is a network representing nine houses that a telecommunications company wants to connect using the minimum cable length (the numbers on the arcs are the distances between houses in meters).
- Apply the Minimal-Spanning Tree technique to determine the path through the network that connects all the houses while minimizing total distance (minimal total cable length). (5 Marks)
- Compute the minimal total distance. (1 Mark)
- What other types of service connections can be done with minimizing the total distance? (1 Mark)
Student’s Name : _______________________________
Student’s ID : _______________________________
ANSWER SHEET
Question 1: Problem solving (10 Marks)
| Average/Total | = 60 | = 138 | Sum = 358 | Sum = -2151 |
- Based on this scatter diagram, how is the relationship between X and Y ? (1 Mark)
- Use the calculations results in the table above to find the values of b0 and b1, and write the simple regression model to predict Y by X. (3 Marks)
- Using the regression model, find the predicted value of Y if X = 70. (2 Marks)
- If SST = 14546, SSE = 1621.97, and SSR = 12924.03, compute the r2 and write down its interpretation. (2 Marks)
- Write down the hypotheses H0 and H1 for testing the significance of the linear relationship between X and Y, and compute the F-statistic. (2 Marks)
Question 2: Problem solving (13 Marks)
- Compute the demand forecast for month 7 using the simple moving average of order 2, then of order 3. Compute the whole series. (4 Marks)
|
- Compute the demand forecast for month 7 using the weighted moving average of order 2, with weights from the most recent month as 10 and 5, then of order 3 with weights from the most recent month as 6, 3, and 1. Compute the whole series. (4 Marks)
| Month | demand (units) | Two-Month Weighted Moving Average | Three-Month Weighted Moving Average |
| 1 | 5,000 | — | — |
| 2 | 6,000 | — | — |
| 3 | 6,500 | — | |
| 4 | 8,000 | ||
| 5 | 9,500 | ||
| 6 | 11,500 | ||
| 7 | — |
- Compute the demand forecast for month 7 using the exponential smoothing, assuming that F1= 4,500 units, with α= 0.2 then with α= 0.3. (5 Marks)
| Month | demand (units) | exponential smoothing sales forecast α= 0.2 | exponential smoothing sales forecast α= 0.3 |
| 1 | 5,000 | 4,500 | 4,500 |
| 2 | 6,000 | ||
| 3 | 6,500 | ||
| 4 | 8,000 | ||
| 5 | 9,500 | ||
| 6 | 11,500 | ||
| 7 | — |
Question 3: Problem solving (10 Marks)
- Represent graphically the feasible region (solution space). (4 Marks)
- Find the Optimal Solution using the graphical method. (4 Marks)
Part II: Answer the following questions:
- Define the special issue of unboundedness, in linear programming problems. (1 Mark)
- Define the special issue of redundancy, in linear programming problems. (1 Mark)
Question 4: Problem solving (7 Marks)
- Apply the Minimal-Spanning Tree technique to determine the path through the network that connects all the houses while minimizing total distance (minimal total cable length). (5 Marks)
- Compute the minimal total distance. (1 Mark)
- What other types of service connections can be done with minimizing the total distance? (1 Mark)