# University of Northern British Columbia Business Program s1

UNIVERSITY OF NORTHERN BRITISH COLUMBIA SCHOOL OF BUSINESS

Commerce 251 F04 Term Exam 2: Monday, November 8th 2004

Chapters 7, 8, Part 9, 10, 15 and 16 and Regression

2. Answer the quantitative questions in the exam book provided

only. Clearly number each question. If you choose to use

pencil then your exam cannot be considered for re-marking.

3. Each multiple choice question is worth 2 1/2 marks for a total

of 25 marks.

4. Each quantitative question is worth 25 marks for a total of 75

Marks.

5. Time allowed is 1 hour and 15 minutes.

1. A product design and market share optimization model involving a sample of 12 customers and 5 product design attributes will require

a. 12 constraints.

b. 17 constraints.

c. 17 variables.

d. 5 variables.

2. Let x1 and x2 be 0 - 1 variables whose values indicate whether projects 1 and 2 are not done or are done. Which answer below indicates that project 2 can be done only if project 1 is done?

a. x1 + x2 = 1

b. x1 + x2 = 2

c. x1 - x2 0

d. x1 - x2 0

3. Sensitivity analysis for integer linear programming

a. can be provided only by computer.

b. has precisely the same interpretation as that from linear programming.

c. does not have the same interpretation and should be disregarded.

d. is most useful for 0 - 1 models.

4. The difference between the transportation and assignment problems is that

a. each supply and demand value is 1 in the assignment problem

b. the number of origins must equal the number of destinations in the transportation problem

c. total supply must equal total demand in the transportation problem

d. there are many differences between the transportation and assignment problems

5. Variables that indicate the distance a target is from the level achieved are called

a. goal variables.

b. target variables.

c. deviation variables.

d. preemptive variables.

6. Time series methods

a. discover a pattern in historical data and project it into the future.

b. include cause-effect relationships.

c. are useful when historical information is not available.

d. All of the alternatives are true.

7. Seasonal components

a. cannot be predicted.

b. are regular repeated patterns.

c. are long runs of observations above or below the trend line.

d. reflect a shift in the series over time.

8. The multiplicative model

a. uses centered moving averages to smooth the trend fluctuations.

b. removes trend before isolating the seasonal components.

c. deseasonalizes a time series by dividing the values by the appropriate seasonal index.

d. provides a unique seasonal index for each observation of the time series.

9 To select a value for α for exponential smoothing

a. use a small α when the series varies substantially.

b. use a large α when the series has little random variability.

c. use any value between 0 and 1

d. All of the alternatives are true.

10. A linear regression model assumes:

a. that variables are independent

b. that values of the dependent variable are normally distributed for a given value of the independent variable

c. that variances in the variable distributions are approximately equal

d. All of the alternatives are true.

Quantitative Problems – (25 marks each)

11. What is the LP model that maximizes the flow through the following network (in at node 1 and out of the network at node 7)? Use the notation xij for the amount of flow from node i to node j.

12. Durham Designs manufactures home furnishings for department stores. Planning is underway for the production of items in the "Wildflower" fabric pattern during the next production period.

Fabric required (yds) / 7 / 4 / 9
Time required (hrs) / 1.5 / 2 / .5
Packaging material / 3 / 2 / 1
Profit / 12 / 10 / 8

Inventory of the Wildflower fabric is 3000 yards. Five hundred hours of production time have been scheduled. Four hundred units of packaging material are available. Each of these values can be adjusted through overtime or extra purchases.

Durham would like to achieve a profit of \$3200, avoid purchasing more fabric or packaging material, and use all of the hours scheduled. What is the goal programming model?

Use the variable symbols B for bedspreads, C for curtains and D for dustruffles.

13. Analysts at a company that produces food preparation appliances notice that sales of 24 similar appliances in the Northern Central Interior have not been up to expectations and wish to explore a forecast model. They have collected data for the 24 items for monthly sales (\$), amount spent on advertising (\$), the number of competitors to the particular type of appliance, the number of discounts (coupons, sales, markdowns etc) offered with the appliance and the warranty offered (years). A portion of the data table appears as follows:

Sales(\$) Advert.(\$) # of Comp. Discounts Warranty(yrs)

4565 459 1 1 2.00

4896 545 0 0 .25

4480 472 2 2 1.00

The correlation table appears as follows:

A step wise regression for the four independent variables appears following:

Model 1:

Model 2:

Model 3:

Model 4:

a) At a 95% confidence interval and considering the correlation table, the coefficient of determination (R2), the F and t statistics, and the values of significant F and P, which (model 1, 2,3 or 4) is the best model? why?

b) What is (write down) the best model?

c) If advertising is \$500, the number of competitors =1, there are no (0) discounts and the warranty offered with the appliance is for 2 years, according to your best model, what is the monthly forecast sales?

UNIVERSITY OF NORTHERN BRITISH COLUMBIA – SCHOOL OF BUSINESS

Comm 251: Introduction to Management Science – F04

Term Exam 2

Name: ______Student Number: ______

☺ Please use pen and place “0” around choice. Do not use whiteout.

1. a b c d

2. a b c d

3. a b c d

4. a b c d

5. a b c d

6. a b c d

7. a b c d

8. a b c d

9. a b c d

10. a b c d

11.

12.

Let B = the number of bedspreads to make

C = the number of curtains to make

D = the number of dustruffles to make

Min d1- + d2+ + d3+ + d4-

s.t. 12B + 10C + 8D + d1- - d1+ = 3200

7B + 4C + 9D + d2- - d2+ = 3000

1.5B + 2C + .5D + d3- - d3+ = 500

3B + 2C + 1D + d4- - d4+ = 400

B, C, D, d1-, d1+, d2-, d2+, d3-, d3+, d4- , d4+ 0

13.

a) the best model is Model number 2.

- has 2 independent variables (fewest – “Parsimony”)

- R2 is 77.9 which is pretty good and F stat is significant

- model 3: advertising has a p value greater than .05 so should not be included.

- model 4: R2 not much improved and advertising and warranty have p greater than .05 so should not be included.

Notice from correlation table that discounts and advertising are highly correlated to each other and to # of competitors so are not likely independent and can be eliminated.

b) model is: Sales (\$) = 5012 – 466(# competitors)+251(Warranty in years)

c) correct answer for model 2 is: \$5047.

However, for the other models:

Model 1: \$4853

Model 3: \$5044

Model 4: \$4965.

Comm 251 F04 Page 3 of 7 Term Exam 2