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# ADMS 3330 Fall 2008 Final Exam + Answers.pdf

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ADMS 3330

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ADMS 3330 FALL 2008 EXAM –All Multiple choice Exam (See Answer Key on last page)
MULTIPLE CHOICE. Choose the letter corresponding to the one alternative that best completes the
statement or answers the question.
1. Which of the following are assumptions or requirements of the transportation problem?
a. goods are the same, regardless of source
b. there must be multiple sources
c. shipping costs per unit do not vary with the quantity shipped
d. all of the above
2. In a trans-shipment problem, items may be transported
a. from source to source
b. from one destination to another
c. from sources to trans-shipment point
d. from trans-shipment points to destinations
e. all of the above
3. An assignment problem is a special form of transportation problem where all supply and demand
values equal
a. 0
b. 1
c. 2
d. greater than 1
e. none of the above
4. The trans-shipment model is an extension of the transportation model in which intermediate trans -
shipment points are between the sources and destinations.
a. decreased
b. deleted
c. subtracted
d. added
5. In the process of evaluating location alternatives, the transportation model method minimizes the
a. total demand
b. total supply
c. total shipping cost
d. number of destinations
6. Arcs in a trans-shipment problem
a. indicate the direction of the flow
b. must connect every node to a trans-shipment node
c. represent the cost of shipments
d. all of the above
7. A trans -shipment constraint must contain a variable for every______________ entering or leaving the
node.
a. leave
b. axe
c.arc
d. flow
Page 1 of 19 ADMS 3330 FALL 2008 EXAM –All Multiple choice Exam (See Answer Key on last page)
8. Transportation, assignment, and trans -shipment problems have wide applications and belong to a
class of linear programming problems called
a. distance problems.
b. network flow problems.
c. distribution design problems.
d. minimum cost problems.
9. The problem which deals with the distribution of good s from several sources to several destinations
is the
a. network problem
b. transportation problem
c. assignment problem
d. trans-shipment problem
10. The parts of a network that represent the origins are
a. the axes
b. the flow
c. the nodes
d. the arrows
11. A linear program where the slope of the objective function is the same as the slope of one of the
constraints results in
a. alternative optimal solutions
b. unique optimal solution
c. infeasibility
d. unbounded feasible region
12. In the linear programming formulation of a transportation network
a. there is one constraint for each node.
b. there is one variable for each arc.
c. the sum of variables corresponding to arcs out of an origin node is constrained by the supply at that
node.
d. All of the alternatives are correct.
13. Constraints in a trans-shipment problem
a. correspond to arcs.
b. include a variable for every arc.
c. require the sum of the shipments out of an origin node to equal supply.
d. All of the alternatives are correct.
14. In a trans-shipment problem, shipments
a. cannot occur between two origin nodes.
b. cannot occur between an origin node and a destination node.
c. cannot occur between a trans-shipment node and a destination node.
d. can occur between any two nodes.
15. The constraint x 14+ x24 — x 47x 48 = 0, can only be a ___________ constraint
a. origin
b. trans-shipment
c. destination
d. all of the above.
Page 2 of 19 ADMS 3330 FALL 2008 EXAM –All Multiple choice Exam (See Answer Key on last page)
16. An unbalanced transportation problem with demand exceeding supply
a. requires a dummy demand
b. requires a dummy supply
c. both a. and b.
d.neither a. nor b.
17. When a route in a transportation problem is unacceptable,
a. the corresponding variable must be removed from the LP formulation.
b. the corresponding variable must be constrained to zero.
c. either a. or b
d. neither a. nor b
Questions #18 through #22. A linear trend analysis was performed on monthly sales (in $000) of a
computer store over the 60 months (x = 1, 2, ..., 60) from January 2004 through December 2008. Below
is partial output from the associated linear regression analysis using a certain statistical package:
Regression Analysis - Linear model: Y = a + b*X
Dependent variable: sales_000
Independent variable: month
Stand T
Parameter Estimate Error Statistic P-Value
Intercept 93.6257 2.55166 36.6921 0.0000
Slope 0.646287 0.0727694 0.0000
Analysis of Variance
Source Sum of Squares Df Mean Square F-Ratio P-Value
----------------------------------------------------------------------------------------------------------------------------------
Model ? 1 7526.28 78.88 0.0000
Residual ? 58 95.4175
Total (Corr.) 13060.5 59
R-squared = 57.6263 percent
Standard Error of Est. = 9.76819
18. The sample coefficient of correlation is approximately:
A. 7.591
B. 0.7591
C. 57.6263
D. 0.576263
E. not possible to determine from available information
19. The sum of squares for error is approximately:
A. 9.76819
B. 13,060.5
C. 7,526.28
D. 5,534.21
Page 3 of 19 ADMS 3330 FALL 2008 EXAM –All Multiple choice Exam (See Answer Key on last page)
20. The value of the test statistic for testing the significan1e of β , is approximately:
A. 8.8813
B. 36.6921
C. 78.88
D. 0
E. none of the above
21. Using the sample regression equation to forecast monthly sales in 2009, the forecast for January
2009 would be approximately:
A. $94,272
B. $132,403
C. $133,049
D. $93,665
E. none of the above
22. The value of the test statistic for testing the significance of ρ would be:
A. approximately 0.759
B. approximately 0.576
C. approximately zero
D. equal to the value of the test statistic for testing the slope
E. not possible to determine from available information
Questions #23 through #27. The manager of North York Furniture Co. has been reviewing weekly
advertising expenditures. During the past six months, all advertisements for the store have appeared in
the local newspaper, Toronto Star. The number of ads per week has varied from one to seven. The sales
staff has been tracking the number of customers who enter the store each week. A simple linear
regression model using the least squares method is being considered to estimate the number of
customers who enter the store within a week, given the number of advertiseme nts appearing in the
local newspaper during the week. Below is partial linear regression analysis output from a certain
statistical package.
Regression Analysis - Linear model: Y = a + b*X
Dependent variable: no_of_customers
Independent variable: no_of_ads
Standard T
Parameter Estimate Error Statisti P-Value
Intercept 296.92 64.3052 4.61735 0.0001
Slope 21.356 14.2833 1.49517 0.1479
Analysis of Variance
Source Sum of Squares Df Mean Square F-Ratio P-Value
Model ? 1 ? 2.24 0.1479
Residual ? 24 ?
Total (Corr.) 463802.0 25
Correlation Coefficient = ?
R-squared = 8.52106 percent
Standard Error of Est. = 132.96
Page 4 of 19 ADMS 3330 FALL 2008 EXAM –All Multiple choice Exam (See Answer Key on last page)
23. If the least squares line were to be used, a point estimator for the expected number of customers in
a week when no advertisement is placed in the local newspaper is approximately
A. 318
B. 0
C. 297
D. 21
24. If the least squares line were to be used, a point estimator for the expected number of customers in
a week when 5 advertisements are placed in the local newspaper is approximately
A. 21
B. 404
C. 107
D. 297
25. The sum of squares for error is approximately
A. 39520.8
B. 424281.2
C. 463802.0
D. not possible to determine from the available information
26. The proportion of the variation in no_of_customers that is explained by the variation in no_of ads is
approximately
A. 0.085
B. 0.915
C. 0.007
D. 0.292
E. not possible to determine from the available information
27. A test of hypothesis concerning the coefficient of correlation ρ with H A: ρ≠0 at the 10% level of
significance
A. is a one-tailed test
B. yields a test statistic value of 4.61735
C. would lead to a decision to reject the null hypothesis
D. would have as decision rule to reject H o if t> 1.711
E. none of the above is true
28. Types of integer programming models are ________________.
a. total/all
b. 0-1
c. mixed
d. all of the above
29. In a ____________ integer model, some solution values for decision variables are integer and others can
be non-integer.
a. total
b. 0 - 1
c. mixed
d. all of the above
Page 5 of 19 ADMS 3330 FALL 2008 EXAM –All Multiple choice Exam (See Answer Key on last page)
30. Which of the following is not an integer linear programming problem?
a. pure integer
b. mixed integer
c. 0- 1 integer
d. continuous
31. In using rounding of a linear programming model to obtain an integer solution, the solution is
a. always optimal and feasible
b. sometimes optimal and feasible
c. always optimal
d. always feasible
e. never optimal and feasible
32. If x + x is less than or equal to 500y and y is 0-1, then x and x will be _____________if y is 0.
1 2 1 1 1 2 1
a. equal to 0
b. less than 0
c. more than 0
d. equal to 500
e. one of the above
33. If a maximization linear programming problem consist of all less -than—or-equal-to constraints
with al l positive coefficients and the objective function consists of all positive objective function
coefficients, then rounding down the linear programming optimal solution values of the decision
variables will_______________ result in a(n) _____________ solution to the integer linear programming
problem.
a. always, optimal
b. always, non-optimal
c. never, non-optimal
d. sometimes, optimal
e. never, optimal
34. If we are solving a 0-1 integer programming problem, the constraint x 1 + x2≤ 1 is a constraint.
a. multiple choice
b. mutually exclusive
c. conditional
d. co-requisite
e. none of the above
35. If we are solving a 0-1 integer programming problem, the constraint x 1 + x2= 1 is a _____constraint.
a. multiple choice
mutually exclusive
c. conditional
d. corequisite
e. none of the above
36. If we are solving a 0-1 integer programming problem, the constraint x 1 ≤x2is a constraint.
a. multiple choice
b. mutually exclusive
c., conditional
d. co-requisite
e. none of the above
Page 6 of 19 ADMS 3330 FALL 2008 EXAM –All Multiple choice Exam (See Answer Key on last page)
37. If we are solving a 0 -1 integer programming problem, the constraint x1 = x2 is a______________
constraint.
a. multiple choice
b. mutually exclusive
c. conditional
d. corequisite
e. none of the above
38. For a maximization integer linear programming problem, f easible solution is ensured by
rounding____________non-integer solution values if all of the constraints are less-than -or equal- to type.
a. up and down
b. up
c. down
d. up or down
39. The linear programming relaxation contains the ______________and the original constraints of the
integer programming problem, but drops all integer restrictions.
a. different variables
b. slack values
c. objective function
d. decision variables
e. surplus variables
40. If the optimal solution to the linear programming relaxation problem is integer, it is______________
to the integer linear programming problem.
a. real solution
b. a degenerate solution
c. an infeasible solution
d. the optimal solution
e. a feasible solution
41. Binary variables are
a. 0 or 1 only
b. any integer value
c. any continuous value
d. any negative integer value
42. Max Z=5x 1+6x 2
Subject to: 17x 1+ 8x 2136
3x 14x 2 36
x1, 2 ≥ 0 and integer
What is the optimal solution?
a.x1=6, x2=4, Z=54
b. x1= 3, x2 6, Z=51
c. x1=2, x2=6, Z=46
d. x1= 4, x2= 6, Z=56
e. x1= 0, x2 9 Z=54
Page 7 of 19 ADMS 3330 FALL 2008 EXAM –All Multiple choice Exam (See Answer Key on last page)
43. Assume that we are using 0-1 integer programming model to solve a capital budgeting problem and
xj = 1 if project j is selected and xj= 0, otherwise.
The constraint (x1 + x2 + x3+ x4≤ 2) means that________________ out of the____________ projects must
be selected.
a. exactly 1, 4
b. exactly 2, 4
c. at least 2, 4
d. at most 2, 4
44. In a 0-1 integer programming model, if the constraint x1-x2 = 0, it means when project 1 is selected,
project _______________ be selected.
a. can also
b. can sometimes
c. can never
d. must also
45. The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff has
4 different machines that can produce this kind of hose. Because these machines are from different
manufacturers and use differing technologies, their specifications are not the same.
Machine Fixed cost to set up production run Variable cost per hose Capacity
1 750 1.25 6000
2 500 1.50 7500
3 1000 1.00 4000
4 300 2.00 5000
Write a constraint to ensure that if machine 4 is used, machine 1 will not be used.
a. Y1+Y4≤ 0
b.y1+Y4=0
c.y1+Y4 ≤1
d. Y1 + Y4 ≥ 0
e. y1+y4 ≥1
46. The solution to the linear programming relaxation of a minimization problem will always
be___________ the value of the integer programming minimization problem.
a. greater than or equal to
b. less than or equal to
c. equal to
d. different than
47. Rounding large values of decision variables to the nearest integer value causes problems than
rounding small values.
a. similar
b. more
c. fewer
d. none of the above
48. In a_________ integer model, the solution values of the decision variables are 0 or 1.
a. total
b. binary
c. mixed
d. all of the above
Page 8 of 19 ADMS 3330 FALL 2008 EXAM –All Multiple choice Exam (See Answer Key on last page)
49. Which of the following correctly describes the focus of the Critical Path Method?
a. To order activities in a project in terms of their completion time to facilitate scheduling of the
activities.
b. To determine when a project should be completed and to schedule when each activity in the project
must begin in order to keep the project on schedule.
c. To estimate the probability of completing a project by a given deadline when the time required to
perform the activity is essentially a random variable.
d. To structure the activities of a project in order to elimin ate or reduce critical. dependencies among
the activities.
50. The term time zero identifies
a. the start time for each activity.
b. the start time for the project.
c. midnight on each work day.
d. days with not wasted effort.
(Items #51 - #61) Newfoundland Steel Corporation [NSC] produces four sizes of steel I -beams: small,
medium, large, and extra large. These beams can be produced on any of three machines: A, B, and C. The
lengths in feet of the I beams that can be produced on the machines per hour areas follows:
I-Beam Machine
Size
A B C
Small 300 600 800
Medium 250 400 700
Large 200 350 600
Extra Large 100 200 300
Each machine can be used up to 40 hours per week, and hourly operating costs of machines A, B, and C
are $30.00, $50.00, and $80.00, respectively. Weekly requirements of the different sizes of I beams are,
respectively, 10,000, 8,000, 6,000, and 6,000 feet.
An analyst has formulated an LP model for this machine scheduling problem, defining the decision
variables as follows:
tjk = number of hours per week that machine j is used to produce I beams of size k
with j = A, B, C
and k = S (small), M (medium), L (large), E (extra large).
Newfoundland Steel Corporation
Minimize 30 TAS + 30 TAM + 30 TAL + 30 TAE + 50 TBS + 50 TBM + 50 TBL + 50 TBE + 80 TCS + 80 TCM
+ 80TCL + 80 TCE
S.T.
1) 1TAS+1TAM+1TAL+1TAE ≤ 40 [Machine A hours per week]
2) 1TBS+1TBM+1TBL+1TBE ≤ 40 [Machine B hours per week]
3) 1TCS+1TCM+1TCL+1TCE ≤ 40 [Machine C hours per week]
4) 300TAS+600TBS+800TCS ≥ 10000[Weekly demand for small I-beams (in feet)]
5) 250TAM+400TBM+700TCM ≥ 8000[Weekly demand for medium I-beams (in feet)]

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