Math301 final exam 2015

Math final exam

Math final exam

1

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Table 8-3

A marketing research firm would like to survey undergraduate and graduate college students about whether or not they take out student loans for their education. There are different cost implications for the region of the country where the college is located and the type of degree. The survey cost table is provided below:

The requirements for the survey are as follows:

1. The survey must have at least 1500 students

2. At least 400 graduate students

3. At least 100 graduate students should be from the West

4. No more than 500 undergraduate students should be from the East

5. At least 75 graduate students should be from the Central region

6. At least 300 students should be from the West

The marketing research firm would like to minimize the cost of the survey while meeting the requirements. Let X₁= # of undergraduate students from the East region, X₂= # of graduate students from the East region, X₃= # of undergraduate students from the Central region, X₄= # of graduate students from the Central region, X₅= # of undergraduate students from the West region, and X₆= # of graduate students from the West region.

7) According to Table 8-3, what is the objective function?

7)

A) Maximize 10X₁+ 12X₂+ 15X₃+ 15X₄+ 18X₅+ 21X₆

B) Maximize 10X₁+ 15X₂+ 12X₃+ 18X₄+ 15X₅+ 21X₆

C) Minimize 10X₁+ 12X₂+ 15X₃+ 15X₄+ 18X₅+ 21X₆

D) Minimize 1500X₁+ 400X₂+ 100X₃+ 500X₄+ 75X₅+ 300X₆

E) Minimize 10X₁+ 15X₂+ 12X₃+ 18X₄+ 15X₅+ 21X₆

8) According to Table 8-3, the constraint that the survey must have at least a total of 1500 students is	8)
expressed as
A) 10X1+ 15X2	+12X3	+18X4	+15X5	+21X6?1500.
B) 10X1+ 15X2	+12X3	+18X4	+15X5	+21X6?1500.
C) X1	+X3	+X5	?1500.
D) X1	+X2	+X3	+X4 +X5 +X6?1500.
E) X1	+X2	+X3	+X4 +X5 +X6?1500.

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9) According to Table 8-3, the constraint that there must be at least 400 graduate students is expressed 9)
as
A) X1 + X2	+X3?400.
B) X1 + X2	+X3	+X4 +X5 +X6?400.
C) X1	+X3	+X5	?400.
D) X1	+X2	+X3	+X4 +X5 +X6?400.
E) X2	+X4	+X6	?400.

10)	According to Table 8-3, the minimum cost is			10)
	A) 20500	B) 19400	C) 18950	D) 19625	E) 20000
11)	Agile Bikes has manufacturing plants in Salt Lake City, Dallas, and Chicago. The bikes are shipped	11)
	to retail stores in Los Angeles, New York, Miami, and Seattle. Information on shipping costs,
	supply, and demand is given in the following table:

What type of mathematical programming is required to solve this problem?

A) Integer programming

B) Nonlinear programming

C) Linear programming

D) Zero-one integer programming

E) Mixed-integer programming

Write your answer in the space provided.

12) A package express carrier is considering expanding the fleet of aircraft used to transport packages. There is a total of $220 million allocated for purchases. Two types of aircraft may be purchased- the C1A and the C1B. The C1A costs $25 million, while the C1B costs $18 million. The C1A can carry 60,000 pounds of packages, while the C1B can only carry 40,000 pounds of packages. The company needs at least eight new aircraft. In addition, the firm wishes to purchase at least twice as many C1Bs as C1As. Formulate this as an integer programming problem to maximize the number of pounds that may be carried.

3

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Table 11-1

The following represents a project with known activity times. All times are in weeks.

Activity	Immediate	Time
Predecessor
A		-	4
B		-	3
C		A	2
D		B	7
E		C, D	4
F		B	5
13) Using the data in Table 11-1, what is the minimum possible time required for completing the	13)
	project?

A) 14

B) 8

C) 10

D) 25

E) None of the above

14) Using the data in Table 11-1, what is the latest possible time that C may be started without	14)
delaying completion of the project?
A) 8
B) 10
C) 0
D) 4
E) None of the above
15) According to Table 11-1, compute the slack time for activity D.	15)
A) 3
B) 0
C) 6
D) 5
E) None of the above
16) Using the data in Table 11-1, compute the latest finish time for activity E.	16)
A) 10

B) 25

C) 4

D) 14

E) None of the above

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Write your answer in the space provided.

The Dean's Office keeps tracks of student complaints received each week. The probability distribution for complaints can be represented as a table as shown below. The random variable x_i represents the number of complaints, and p(x_i) is the probability of receiving x_i complaints.

xi	0	1	2	3	4	5	6
p(xi)	.10	.15	.18	.20	.20	.10	.07

17) What is the probability that they receive less than 3 complaints in a week?

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

18) At a university with 1,000 business majors, there are 200 business students enrolled in an	18)
introductory statistics course. Of these 200 students, 50 are also enrolled in an introductory
accounting course. There are an additional 250 business students enrolled in accounting but not
enrolled in statistics. If a business student is selected at random, what is the probability that the
student is either enrolled in accounting or statistics, but not both?
A) 0.05
B) 0.45
C) 0.40
D) 0.50
E) None of the above
19) At a university with 1,000 business majors, there are 200 business students enrolled in an	19)
introductory statistics course. Of these 200 students, 50 are also enrolled in an introductory
accounting course. There are an additional 250 business students enrolled in accounting but not
enrolled in statistics. If a business student is selected at random, what is the probability that the
student is enrolled in accounting?
A) 0.50
B) 0.25
C) 0.20
D) 0.30
E) None of the above
20) At a university with 1,000 business majors, there are 200 business students enrolled in an	20)
introductory statistics course. Of these 200 students, 50 are also enrolled in an introductory
accounting course. There are an additional 250 business students enrolled in accounting but not

enrolled in statistics. If a business student is selected at random, what is the probability that the student is enrolled in statistics?

A) 0.20

B) 0.05

C) 0.30

D) 0.25

E) None of the above

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21) At a university with 1,000 business majors, there are 200 business students enrolled in an	21)
introductory statistics course. Of these 200 students, 50 are also enrolled in an introductory
accounting course. There are an additional 250 business students enrolled in accounting but not
enrolled in statistics. If a business student is selected at random, what is the probability that the
student is enrolled in both statistics and accounting?
A) 0.05
B) 0.25
C) 0.20
D) 0.06
E) None of the above
22) At a university with 1,000 business majors, there are 200 business students enrolled in an	22)
introductory statistics course. Of these 200 students, 50 are also enrolled in an introductory
accounting course. There are an additional 250 business students enrolled in accounting but not
enrolled in statistics. If a business student is selected at random and found to be enrolled in
statistics, what is the probability that the student is also enrolled in accounting?
A) 0.30
B) 0.05
C) 0.25
D) 0.20
E) None of the above
23) At a university with 1,000 business majors, there are 200 business students enrolled in an	23)
introductory statistics course. Of these 200 students, 50 are also enrolled in an introductory
accounting course. There are an additional 250 business students enrolled in accounting but not
enrolled in statistics. If a business student is selected at random, what is the probability that the
student is enrolled in neither accounting nor statistics?
A) 0.45
B) 0.05
C) 0.55
D) 0.50
E) None of the above
24) At a university with 1,000 business majors, there are 200 business students enrolled in an	24)
introductory statistics course. Of these 200 students, 50 are also enrolled in an introductory

accounting course. There are an additional 250 business students enrolled in accounting but not enrolled in statistics. If a business student is selected at random, what is the probability that the student is not enrolled in statistics?

A) 0.05

B) 0.25

C) 0.80

D) 0.20

E) None of the above

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25) Data for a particular subdivision near downtown Houston indicate that the average price per	25)
square foot for a home is $100 with a standard deviation of $5 (normally distributed). What is the
probability that the average price per square foot for a home is greater than $110?
A) 0.841
B) 0.023
C) 0
D) 0.977
E) None of the above
26) Data for a particular subdivision near downtown Houston indicate that the average price per	26)
square foot for a home is $100 with a standard deviation of $5 (normally distributed). What is the
probability that the average price per square foot for a home is less than $85?
A) 0.618

B) 0.999

C) 0.001

D) 0.382

E) None of the above

Write your answer in the space provided.

27) A market research study is being conducted to determine if a product modification will be well received by the public. A total of 1,000 consumers are questioned regarding this product.

The table below provides information regarding this sample.

	Positive	Neutral	Negative
	Reaction	Reaction	Reaction
Male	240	60	100
Female	260	220	120

(a) What is the probability that a randomly selected male would find this change unfavorable (negative)?

(b) What is the probability that a randomly selected person would be a female who had a positive reaction?

(c) If it is known that a person had a negative reaction to the study, what is the probability that the person is male?

28) In a production run of 300 units, there are exactly 20 defective items and 280 good items.

(a) What is the probability that a randomly selected item is defective?

(b) If two items are sampled without replacement, what is the probability that both are good?

(c) If two items are randomly sampled without replacement, what is the probability that the first is good but the second is defective?

7

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

29) The following is a payoff table giving profits for various situations.

29)

What decision would an optimist make?

A) Alternative 1

B) Alternative 2

C) Alternative 3

D) Do Nothing

E) State of Nature A

30) The following is a payoff table giving profits for various situations.

30)

What decision would a pessimist make?

A) Alternative 1

B) Alternative 2

C) Alternative 3

D) Do Nothing

E) State of Nature A

31) The following is an opportunity loss table.

31)

What decision should be made based on the minimax regret criterion?

A) Alternative 1

B) Alternative 2

C) Alternative 3

D) State of Nature A

E) Does not matter

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32) The following is a payoff table.

32)

What decision should be made based on the minimax regret criterion?

A) Alternative 1

B) Alternative 2

C) Alternative 3

D) State of Nature C

E) Does not matter
33) Dr. Mac, a surgeon, must decide what mode of treatment to use on Mr. Samuels. There are three	33)

modes of treatment: Mode A, B, and C; and three possible states of nature: 1. Treatment succeeds and patient leads a normal life, 2. Patient survives treatment but is permanently disabled, and 3. Patient fails to survive treatment. Dr. Mac has prepared the decision table below. What mode of treatment maximizes the expected value?

A) Normal Life

B) Mode A

C) Mode B

D) Mode C

E) All three treatments are equally desirable.

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34) The following is a payoff table giving profits for various situations.

34)

The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively. If a perfect forecast of the future were available, what is the expected value with this perfect information?

A) 36

B) 130

C) 166

D) 160

E) None of the above

Write your answer in the space provided.

35) Demand for a particular type of battery fluctuates from one week to the next. A study of the last six weeks provides the following demands (in dozens): 4, 5, 3, 2, 8, 10 (last week).

(a) Forecast demand for the next week using a two-week moving average.

(b) Forecast demand for the next week using a three-week moving average.

36) Daily high temperatures in the city of Houston for the last week have been: 93, 94, 93, 95, 92, 86, 98 (yesterday).

(a) Forecast the high temperature today using a three-day moving average.

(b) Forecast the high temperature today using a two-day moving average.

(c) Calculate the mean absolute deviation based on a two-day moving average, covering all days in which you can have a forecast and an actual temperature.

37) Use simple exponential smoothing with ?= 0.3 to forecast battery sales for February through May. Assume that the forecast for January was for 22 batteries.

Month	Automobile
Battery Sales
January	42
February	33
March	28
April	59

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38) Use simple exponential smoothing with ?= 0.33 to forecast the tire sales for February through May. Assume that the forecast for January was for 22 sets of tires.

Month	Automobile
Battery Sales
January	28
February	21
March	39
April	34

39) The following table represents the new members that have been acquired by a fitness center.

Month	New members
Jan	45
Feb	60
March	57
April	65

Assuming ?= 0.3, ?= 0.4, an initial forecast of 40 for January, and an initial trend adjustment of 0 for January, use exponential smoothing with trend adjustment to come up with a forecast for May on new members.

Consider the following annual sales data for 2001-2008:

Year	Sales
2001	2
2002	4
2003	10
2004	8
2005	14
2006	18
2007	17
2008	20

40) Use the linear regression method and determine the estimated sales equation.

41) Calculate the coefficient of determination.

42) Calculate the correlation coefficient.

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