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Experience: BA (Hons) in Mathematics from Oxford University

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Urgent Math help please...MAT 540 Quantitative Methods

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Question 1

Management science techniques focus primarily on observation, model construction and implementation to find an appropriate solution to a problem.

True

False

Question 2

In linear programming problems, multiple optimal solutions occur when constraints are parallel to each other.

True

False

Question 3

A change in the value of an objective function coefficient will always change the value of the optimal solution.

True

False

Question 4

Fractional relationships between variables are not permitted in the standard form of a linear program.

True

False

Question 5

In a total integer model, all decision variables have integer solution values.

True

False

Question 6

In a transshipment problem, items may be transported from destination to destination and from source to source.

True

False

Question 7

The events in an experiment are mutually exclusive if only one can occur at a time.

True

False

Question 8

The minimax criterion minimizes the maximum payoff.

True

False

Question 9

Excel can be used to simulate systems that can be represented by both discrete and continuous random variables.

True

False

Question 10

Adjusted exponential smoothing is an exponential smoothing forecast adjusted for seasonality.

True

False

Question 11

Which of the following is an equation or an inequality that expresses a resource restriction in a mathematical model?

*a decision variable

*a parameter

*an objective function

*a constraint

Question 12

If the price decreases but fixed and variable costs do not change, the break even point:

decreases

increases

remains the same

may increase or decrease, depending on sales

Question 13

A slack variable :

is the amount by which the left side of a ≥ constraint is larger than the right side

is the amount by which the left side of a ≤ constraint is smaller than the right side

is the absolute value of the difference between the left and right side of a constraint

all of the above

Question 14

Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the storage space constraint?

90B + 100M ≥ 18000

90B + 100M ≤ 18000

100B + 90M ≤ 18000

500B + 300M ≤ 18000

Question 15

The following is an Excel “Answer” and “Sensitivity” reports of a linear programming problem:

The Answer Report:

The Sensitivity Report:

Which additional resources would you recommend to be increased?

mix/mold

kiln

paint and seal

Cannot tell from the information provided

Question 16

Given the following linear programming problem that minimizes cost.

Min Z = 2x + 8y

Subject to 8x + 4y ≥ 64

2x + 4y ≥ 32

y ≥ 2

What is the sensitivity range for the third constraint, y ≥ 2?

0 to 4

2 to 5.33

0 to 5.33

4 to 6.33

Question 17

Compared to blending and product mix problems, transportation problems are unique because:

They maximize profit.

The constraints are all “=” constraints with no "≤" or "≥" constraints.

The solution values are always integers.

All of the above are True.

Question 18

The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B which cost 50 cents and 75 cents per pound, respectively. Five essential ingredients are contained in the feed, shown in the table below. The table also shows the minimum daily requirements of each ingredient.

Ingredient

Percent per pound in Feed A

Percent per pound in Feed B

Minimum daily requirement (pounds)

1

20

24

30

2

30

10

50

3

0

30

20

4

24

15

60

5

10

20

40

The constraint for ingredient 3 is:

5A + .75B = 20

3B = 20

3 B≤ 20

3B ≥ 20

Question 19

The Wiethoff Company has a contract to produce garden hoses for a customer. Wiethoff has 4 different machines that can produce this kind of hose. Write a constraint to ensure that if machine 4 is used, machine 1 will not be used.

Y1 + Y4 ≤ 0

Y1 + Y4 = 0

Y1 + Y4 ≤ 1

Y1 + Y4 ≥ 1

Question 20

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint.

multiple choice

mutually exclusive

conditional

corequisite

Question 21

The following table represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A, B, or C.

The constraint that represents the quantity demanded by Customer B is:

6X1B + 2X2B + 8X3B ≤ 350

6X1B + 2X2B + 8X3B = 350

X1B + X2B + X3B ≤ 350

X1B + X2B + X3B = 350

Question 22

A professor needs help from 3 student helpers to complete 4 tasks. The first task is grading; the second is scanning; the third is copying, and the fourth is organizing student portfolios. The estimated time for each student to do each task is given in the matrix below.

Which of the following constraints represents the assignment for student A?

XA1 +XA2 + XA3 + XA4 = 0

XA1 +XA2 + XA3 + XA4 = 1

XA1 +XA2 + XA3 + XA4 ≥ 1

XA1 +XA2 + XA3 + XA4 ≥ 0

Question 23

Mutually exclusive events are:

events with distinct probabilities

events that have no outcomes in common

events that have no effect on each other

all of the above

Question 24

Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y. What is the probability that Jim will not be accepted at either university?

*.20

*.30

*.36

*.44

Question 25

Determining the worst payoff for each alternative and choosing the alternative with the best worst is called :

maximin

minimin

maximax

minimax

Question 26

A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

The conservative strategy is:

Buy

Rent

Lease

Brisk.

Question 27

For the following frequency distribution of demand, the random number 0.8177 would be interpreted as a demand of:

0

1

2

3

Question 28

In the Monte Carlo process, values for a random variable are generated by __________ a probability distribution.

sampling from

running

integrating

implementing

Question 29

Given an actual demand of 59, a previous forecast of 64, and an alpha of .3, what would the forecast for the next period be using simple exponential smoothing?

36.9

57.5

60.5

62.5

Question 30

__________ moving averages react more slowly to recent demand changes than do __________ moving averages.

Longer-period, shorter-period

Shorter-period, longer-period

Longer-period, longer-period

Shorter-period, shorter-period

Question 31

A production process requires a fixed cost of $50,000. The variable cost per unit is $25 and the revenue per unit is projected to be $45. Find the break-even point.

Answer: _________________

Question 32

Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and $30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table.

Formulation:

Let x = number of tractors produced per period

y = number of lawn mowers produced per period

MAX 30x + 30y

subject to 2 x + y ≤ 60

2 x + 3y ≤ 120

x ≤ 45

x, y ≥ 0

The graphical solution is shown below.

What is the shadow price for fabrication? Write your answers with two significant places after the decimal and do not include the dollar “$” sign.

Answer: ________________

Question 33

Consider the following linear program, which maximizes profit for two products, regular (R), and super (S):

MAX

50R + 75S

s.t.

1.2R + 1.6 S ≤ 600 assembly (hours)

0.8R + 0.5 S ≤ 300 paint (hours)

.16R + 0.4 S ≤ 100 inspection (hours)

Sensitivity Report:

Cell

Name

Final Value

Reduced Cost

Objective Function

Allowable Increase

Allowable Decrease

$B$7

Regular=

291.67

0.00

50

70

20

$C$7

Super=

133.33

0.00

75

50

43.75

Cell

Name

Final Value

Shadow Price

Constraint R.H. Side

Allowable Increase

Allowable Decrease

$E$3

Assembly (hr/unit)

563.33

0.00

600

1E+30

36.67

$E$4

Paint (hr/unit)

300.00

33.33

300

39.29

175

$E$5

Inspect (hr/unit)

100.00

145.83

100

12.94

40

A change in the market has increased the profit on the super product by $5. Total profit will increase by __________. Write your answer as an integer and do not include the dollar “$” sign.

Answer : _____________

Question 34

Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel’s cat food is made by mixing two types of cat food to obtain the “nutritionally balanced cat diet.” The data for the two cat foods are as follows:

Kitty Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the optimal cost of this plan? Write your answers with two significant places after the decimal and do not include the dollar “$” sign.

Answer: ______________

Question 35

Find the optimal Z value for the following problem. Do not include the dollar “$” sign with your answer.

MAX Z = 5x1 + 8x2

s.t. x1 + x2 ≤ 6

5x1 + 9x2 ≤ 45

x1, x2 ≥ 0 and integer

Answer: ____________

Question 36

A company markets educational software products, and is ready to place three new products on the market. Past experience has shown that for this particular software, the chance of “success” is 80%. Assume that the probability of success is independent for each product. Find the probability that at least two of the three is successful. Round your result to four significant places after the decimal.

Answer: ___________

Question 37

The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What are the expected net revenues for the number of workers he will decide to hire? Do not include the dollar “$” sign with your answer.

Answer: ___________

Question 38

An investor is consider 4 different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below.

.

. Economic Condition

. Poor Average Good Excellent

. Investment (S1) (S2) (S3) (S4)

. A 50 75 20 30

. B 80 15 40 50

. C -100 300 -50 10

. D 25 25 25 25

.

Suppose all states of the world are equally likely (each state has a probability of 0.25). What is the expected value of perfect information? Round your answer to the nearest integer.

Answer: _____________

Question 39

Consider the following decision tree. The objective is to choose the best decision among the two available decisions A and B. Find the expected value of the best decision. Do not include the dollar “$” sign with your answer.

Answer: ______________

Question 40

Recent past demand for product ZXT is given in the following table.

Month

Actual Demand

February

20

March

22

April

33

May

35

June

31

July

48

August

41

The forecasted demand for May, June, July, August, and September are 25, 30, 33, 38, and 40 respectively. Determine the value of MAD. Round your result to four significant places after the decimal.

1. False 2. False 3. False 4. True 5. True 6. True 7. True 8. False 9. True 10. False 11. *a constraint 12. increases 13. is the amount by which the left side of a ≤ constraint is smaller than the right side 14. 100B + 90M ≤ 18000 15. kiln 16. 0 to 5.33 17. The solution values are always integers. 18. 3B ≥ 20 19. Y1 + Y4 ≤ 1 20. corequisite

Great! got them. On # XXXXX the questions asks us to put the answer in this form: Write your answers with two significant places after the decimal and do not include the dollar “$” sign. Your answer was $3.5, After I remove the $ sign what would be the answer with two significant places after the decimal. Thank you.

Customer:replied 4 years ago.

Also, on #36 we are asked to round our result to four significant places after the decimal. Your answer was 0.896. Please correct this for me if you can. The automated system which corrects our assignments is very picky and I do not want the answer to be marked incorrect. Thanks.

Customer:replied 4 years ago.

#32 you put the answer as 0. Are you sure the answer is 0 for the shadow price for fabrication? I am only having issues with Questions 32, 34, and 36. The rest of your answers look good. Please get back to me regarding these three answers. Thanks once again.

Hi. Thanks for your help. I appreciate it. Just wanted to let you know however, that I got 10 answers wrong. #32 being one of them. The answer was not 0. It was 7.50. Here are the correct answers to the questions I got wrong:

13) correct answer: all of the above 23) events that have no outcomes in common 26) Lease 27) 2 32) 7.50 34) 3.60 35) 40 36) 0.8960 (I got your response to follow-up questions a little late so I had to submit my test before I ran out of time)

Nonetheless. I am sure that a lot of effort was placed in solving each answer regardless of the fact that some of them were wrong. I ended up getting an overall of 75% on the test. I will click accept. Thank you once again for you effort.

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