Quantitative Business Analysis Assignment | Get Paper Help

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

Student’s Name
Student’s ID
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

 

 

 

 

 

 

 

 

 

 

 

 

1. Based on this scatter diagram, how is the relationship between X and Y ? (1 Mark)
2. 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)
3. Using the regression model, find the predicted value of Y if X = 70. (2 Marks)
4. If SST = 14546, SSE = 1621.97, and SSR = 12924.03, compute the r² and write down its interpretation. (2 Marks)
5. 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	—

 

1. 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)
2. 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)
3. 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

1. Represent graphically the feasible region (solution space). (4 Marks)
2. Find the Optimal Solution using the graphical method. (4 Marks)

Part II: Answer the following questions:

1. Define the special issue of unboundedness, in linear programming problems. (1 Mark)
2. 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).

 

 

 

 

1. 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)
2. Compute the minimal total distance. (1 Mark)
3. 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

 

 

 

 

 

 

 

 

1. Based on this scatter diagram, how is the relationship between X and Y ? (1 Mark)

 

 

 

 

2. 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)

 

 

 

 

 

 

 

 

3. Using the regression model, find the predicted value of Y if X = 70. (2 Marks)

 

 

 

 

 

4. If SST = 14546, SSE = 1621.97, and SSR = 12924.03, compute the r² and write down its interpretation. (2 Marks)

 

 

 

 

 

 

 

 

5. 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)

1. 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)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Month demand (units) Two-Month Moving Average Three-Month Moving Average 1 5,000 — — 2 6,000 — — 3 6,500 — 4 8,000 5 9,500 6 11,500 7 —

 

 

 

 

 

2. 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	—

 

3. 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)

 

1. Represent graphically the feasible region (solution space). (4 Marks)

 

2. Find the Optimal Solution using the graphical method. (4 Marks)

 

 

 

 

 

 

 

 

 

 

 

Part II: Answer the following questions:

3. Define the special issue of unboundedness, in linear programming problems. (1 Mark)

 

 

4. Define the special issue of redundancy, in linear programming problems. (1 Mark)

 

 

 

 

 

 

Question 4: Problem solving (7 Marks)

1. 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)
2. Compute the minimal total distance. (1 Mark)

 

 

 

 

3. What other types of service connections can be done with minimizing the total distance? (1 Mark)