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quantitative methods quiz quantitative methods quiz

Date added: 09/09/2012
Date modified: 09/09/2012
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•    Question 1


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




•    Question 2


In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 – x2 = 0 implies that if project 2 is selected, project 1 cannot be selected.




•    Question 3


In an unbalanced transportation model, supply does not equal demand and one set of constraints uses = signs.




•    Question 4


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




•    Question 5


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




•    Question 6


Validation of a simulation model occurs when the true steady state average results have been reached.




•    Question 7


In a break-even model, if all of the costs are held constant, how does an increase in price affect the model?
Breakeven point decreases
Breakeven point decreases

•    Question 8


An equation or inequality that expresses a resource restriction in a mathematical model is called _____________________.
a constraint.

a constraint.


•    Question 9


Using the maximin criterion to make a decision, you
Look at the worst payoff for each possible decision and select the decision with the largest worst payoff
Look at the worst payoff for each possible decision and select the decision with the largest worst payoff

•    Question 10


The probability of observing x
successes in a fixed number of trials is a problem related to
the binomial distribution
the binomial distribution

•    Question 11


In linear programming problems, multiple optimal solutions occur
when the objective function is parallel to a constraint line
when the objective function is parallel to a constraint line

•    Question 12


Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. What is the storage space constraint?
100B + 80M  =  18000
100B + 80M  =  18000

•    Question 13


Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. What is the objective function?
Max Z = 85B + 75M
Max Z = 85B + 75M

•    Question 14





The Sensitivity Report: 


Which additional resources would you recommend to be increased?
kiln
kiln

•    Question 15


For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs., and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the:
same product mix, different total profit
same product mix, different total profit

•    Question 16


Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demands for gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraint for component 1.
x11 + x12 = 8000
x11 + x12 = 8000

•    Question 17


In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively.  The investor has up to $50,000 to invest. The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased.  Which constraint is correct?
X1 = 0.35(X1 + X2 + X3)
X1 = 0.35(X1 + X2 + X3)

•    Question 18


In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation?
x1 + x5 = 1,    x2 + x5 = 1
x1 + x5 = 1,    x2 + x5 = 1

•    Question 19


The Kirschner Company has a contract to produce garden hoses for a customer. Kirschner has 5 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 = 1
Y1 + Y4 = 1

•    Question 20


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:
X1B + X2B + X3B = 350

X1B + X2B + X3B = 350


•    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 supplied by DC 1 is:
X1A + X1B + X1C = 500
X1A + X1B + X1C = 500

•    Question 22


Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot.  Assume also that this time is normally distributed with a standard deviation of 2 minutes. What percentage of the students will take between 2 and 6 minutes to find a parking spot in the main parking lot?
62.47%

62.47%


•    Question 23


79
75

•    Question 24


Consider the following graph of sales.



Which of the following characteristics is exhibited by the data?
Trend plus irregular
Trend plus irregular

•    Question 25


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


0
2

•    Question 26


A bakery is considering hiring another clerk to better serve customers.  To help with this decision, records were kept to determine how many customers arrived in 10-minute intervals.  Based on 100 ten-minute intervals, the following probability distribution and random number assignments developed.

Number of Arrivals    Probability    Random numbers
6    .1    .01 - .10
7    .3    .11 - .40
8    .3    .41 - .70
9    .2    .71 - .90
10    .1    .91 - .00











Suppose the next three random numbers were .18, .89 and .67.  How many customers would have arrived during this 30-minute period?
24
24

•    Question 27


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

•    Question 28

Ford’s Bed & Breakfast  breaks even if they sell 50 rooms each month.  They have a fixed cost of $6500 per month.  The variable cost per room is $30.  For this model to work, what must be the revenue per room? 



•    Question 29

Nixon’s Bed and Breakfast has a fixed cost of $5000 per month and the revenue they receive from each booked room is $200.  The variable cost per room is $75.  How many rooms do they have to sell each month to break even



•    Question 30

Students are organizing a "Battle of the Bands" contest.  They know that at least 100 people will attend.  The rental fee for the hall is $200 and the winning band will receive $500.  In order to guarantee that they break even, how much should they charge for each ticket?




•    Question 31


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.








•    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.









•    Question 33


Klein 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:

Cat Food    Cost/oz    protien (%)    fat (%)
Partner's Choice    $0.20    45    20
Feline Excel    $0.15    15    30






•    Question 34



MAX Z = 5x1 + 8x2
s.t.             x1 + x2 = 6
5x1 + 9x2 = 45
x1, x2 = 0 and integer



•    Question 35



0.11
.10
.11


•    Question 36


Mr. Sartre is considering four different opportunities, A, B, C, or D.  The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below.


Investment    Economic Conditions
Poor
(S1)    Average
(S2)    Good
(S3)    Excellent
(S4)
A    38    25    33    10
B    10    15    20    85
C    20    100    20    -25
D    25    25    100    25






•    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 is the expected value of perfect information? Do not include the dollar “$” sign with your answer. The following payoff table is given in thousands of dollars (e.g. 50 = $50,000).  






•    Question 38

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? The following payoff table is given in thousands of dollars (e.g. 50 = $50,000). 







•    Question 39


The following sales data are available for 2003-2008 :

Year    Sales    Forecast
2003    7    7
2004    8    8.5
2005    12    10.5
2006    14    13
2007    16    15
2008    18    16


Calculate the MAPD and express it in decimal notation. Please express the result as a number with 4 decimal places.  If necessary, round your result accordingly.  For instance, 9.14677, should be expressed as 9.1468



•    Question 40

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.       

quantitative methods quantitative methods

Date added: 07/09/2012
Date modified: 07/09/2012
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Question 1   
If two events are not mutually exclusive, then P(A or B) = P(A) + P(B)
Question 2
Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is normally distributed.
Question 3
Probability trees are used only to compute conditional probabilities.
Question 4
The maximin approach involves choosing the alternative with the highest or lowest payoff.
Question 5
The minimin criterion is optimistic.
Question 6
The minimax regret criterion maximizes the minimum regret.
Question 7
The Hurwicz criterion is a compromise between the minimax and minimin criteria.
Question 8
Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot.  Assume also that this time is normally distributed with a standard deviation of 2 minutes. Find the probability that a randomly selected college student will take between 2 and 6 minutes to find a parking spot in the main parking lot.
0.6247
0.6247
Question 9
83
83
Question 10
The chi-square test is a statistical test to see if an observed data fit a _________.
particular probability distribution
All of the above
Question 11
The maximin criterion results in the
maximum of the minimum payoffs
maximum of the minimum payoffs
Question 12
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 maximin strategy is:
Lease
Lease
Question 13
A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in.  Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.                   
Weather
Cold    Warm  Rainy
S1      S2               S3
Bike:   A1      10          8           6
Hike:  A2      14        15           2
Fish:   A3        7          8           9
If the group chooses to minimize their maximum regret, what activity will they choose?
A3
Any of the above
Question 14
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 maximax strategy is:
Buy
Buy
Question 15
0.0402
0.0400
.0401
.0402
.0400
Question 16
A brand of television has a lifetime that is normally distributed with a mean of 7 years and a standard deviation of 2.5 years. What is the probability that a randomly chosen TV will last more than 8 years? Write your anwsers with two places after the decimal.
0.3447
0.3445
.3446
.3447
.3445
Question 17
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.
If the probability of brisk business is .40, what is the numerical maximum expected value?
Question 18
The quality control manager for ENTA Inc. must decide whether to accept (a1), further analyze (a2) or reject (a3) a lot of incoming material. Assume the following payoff table is available. Historical data indicates that there is 30% chance that the lot is poor quality (s1), 50 % chance that the lot is fair quality (s2) and 20% chance that the lot is good quality (s3).
What is the numerical value of the minimax regret?
Question 19
A manager has developed a payoff table that indicates the profits associated with a set of alternatives under 2 possible states of nature.
Alt       S1           S2
1          10             2
2          -2              8
3            8             5
What is the highest expected value? Assume that the probability of S2 is equal to 0.4.
Question 20
A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in.  Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.                   
Weather
Cold    Warm  Rainy
S1      S2               S3
Bike:   A1      10          8           6
Hike:  A2      14        15           2
Fish:   A3        7          8           9
If the probabilities of cold weather (S1), warm weather (S2), and rainy weather (S3) are 0.2, 0.4, and 0.4, respectively what is the EVPI for this situation?

Maths quiz 2 Maths quiz 2

Date added: 07/08/2012
Date modified: 07/08/2012
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Maths Quiz 1 Maths Quiz 1

Date added: 07/08/2012
Date modified: 07/08/2012
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Q1
Question 1
A child's height h (in inches) closely resembles a linear function in terms of the child's age a (in years) if the child is between the ages of 5 and 10. The height of a certain youngster is 46 inches when the child is age 5, and 55 inches at age 7. Find a linear function relating a child's height h to his or her age a.

Q2
Question 2
An observer, standing on level ground, 115 feet from the bottom of a tower, looks at the top of the tower and notices that his angle of elevation is 0.5 radians. Estimate the height, h, of the tower, rounding your answer to the nearest tenth.

A)    h = 62.8 feet
B)    h = 75.3 feet
C)    h = 81.1 feet
D)    h = 86.9 feet

Q3
Question 3Rewrite as a single logarithm and simplify, if possible.

Q4
Question 4
Determine the limit.   
Answer with a number,  ,   or that the limit does not exist.

Q5
Question 5
Suppose the length of an animal t days after birth is given by h(t).
What is the length of the animal at birth?

Q6
Question 6
Determine all vertical and slant asymptotes.
A)    vertical asymptotes:     slant asymptote: 

B)    vertical asymptote:   slant asymptote: 

C)    vertical asymptote:   slant asymptote: 

D)    vertical asymptotes:     slant asymptote: 


Q7
Question 7
Find the equation of the tangent line to   at 

Q8
Question 8
Find the derivative of  .

Q9
Question 9
A bacterial population starts at 300 and quadruples every day. Calculate the percent rate of change rounded to 2 decimal places.
A)    160.94 %
B)    138.63 %
C)    1.39 %
D)    88.63 %

Q10
Question 10
Suppose a snowball melts in such a way that it maintains a spherical shape. If the radius is decreasing at a rate of 1.75 cm per hour when the radius is 6 cm, how fast is the volume of the snowball decreasing at that instant?
A)    791.7 cm3/hr
B)    263.9 cm3/hr
C)    583.2 cm3/hr
D)    1045.0 cm3/hr

Q11
Question 11
The total cost of producing and marketing x number of units of a certain product is given by  . For what number x is the total cost a minimum? Round answer to nearest unit.

Q12
Question 12
Given the graph of  , locate the absolute extrema (if they exist) on the interval  .
A)    absolute max: 

B)    absolute min: 

C)    absolute min: 

D)    no absolute extrema

Q13
Question 13
Find an antiderivative by reversing the chain rule, product rule or quotient rule.

Q14
Question 14
Find the position function   from the given velocity function and initial value. Assume that units are feet and seconds.

Q15
Question 15
Evaluate the integral.

Q16
Question 16
Evaluate the derivative using properties of logarithms where needed.

Q17
Question 17
Identify the graph and the area bounded by the curves   on the interval  .


Q18
Question 18
When pumping water out of a full hemispherical basin with radius r feet, how far down will the water level be when 1/5 of the work has been done? [The density of water is 62.4 lbs/ft3.]


Q19
Question 19
Find the volume of the solid with cross-sectional area   extending over the range  .

Q20
Question 20
Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by   abouty = 10.

Math Quiz 3 Math Quiz 3

Date added: 07/09/2012
Date modified: 07/09/2012
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Math Quiz 3Q1
Question 1
A bank offers to sell a bank note that will reach a maturity value of $12,000 in 12 years. How much should you pay for it now if you wish to receive an 8% return on your investment?

1)    $925.93
2)    $4594.71
3)    $11,040.00
4)    $920.00

Q2
Question 2
In 1995 an investor put $2000 in an account which paid 8%. In 2005 she withdrew $1000 from the account. What will the account be worth in 2020 ?

1)    $13,778.11
2)    $11,458.00
3)    $7389.06
4)    $3451.08

Q3
Question 3
The Polymerase Chain Reaction (PCR) is used to replicate segments of DNA. It is used to make DNA samples big enough for testing, starting from very small samples collected, for instance, from a crime scene. PCR can double the number of a particular DNA segment every two minutes. If one wants a DNA sample with   copies of a particular segment, how long must the PCR process be carried out to produce them? Assume that there is just one segment in the original sample.

1)    106 minutes
2)    53 minutes
3)    18 minutes
4)      minutes


Q4
Question 4        4 / 4 points
An electrical power supply, such as a battery, generates an electrical potential (voltage, V) which varies depending on how much current (i) it is delivering. The integral   represents the total power (energy per unit time) being given off by the battery when it is producing a current I. The useful electricalpower, however, is just the product  . The difference between the total and the electrical power represents power that is wasted (and that accumulates as heat). Consider a hypothetical battery with a voltage vs. current curve described by the equation  .   If the battery is producing a current of 4 amperes, how much electrical power is being produced, and how much power is being wasted?

Q5
Question 5        4 / 4 points
Evaluate the integral by computing the limit of Riemann sums.

Q6
Question 6        4 / 4 points
The population of New Zealand grew exponentially through the 20th century at a rate of 1.6%   . If the population in 2000 was 3.9 million, when was the population 1.0 million?

1)    1915
2)    1920
3)    1925
4)    1930

Q7
Question 7        4 / 4 points
Find the solution of the differential equation,  , satisfying the initial condition,  .

Q8
Question 8        4 / 4 points
Ba has a half-life of 2.5 hours. How long would it take for 35 mg of  Ba in a sample to decay to 1.0 mg?

1)    87.5 hours
2)    8.9 hours
3)    3.6 hours
4)    12.8 hours

Q9
Question 9        4 / 4 points
Bubba, a farmer, wants to build a pen using the 20 ft   40 ft corner of his barn as part of the pen as shown in the figure below (the corner will not require any fencing). If Bubba has 128 ft of available fencing, then what will be the maximum area?

1)    2209 square feet
2)    1764 square feet
3)    1369 square feet
4)    1024 square feet

Q10
Question 10        4 / 4 points
Determine whether or not the integral is improper.

1)    The integral is improper.  

2)    The integral is not improper.

Q11
Question 11        4 / 4 points
Find the solution to the following separable differential equation.

Q12
Question 12        4 / 4 points
Find the solution of the differential equation,  , satisfying the initial condition,  .

Q13
Question 13        4 / 4 points
$50,000 that was invested in 1990 was worth $134,100 in 2000. What annual interest rate did the investment earn in that 10 year period? Assume continuous compounding.

1)    118.06%
2)    10.91%
3)    108.20%
4)    9.87%

Q14
Question 14        4 / 4 points
Find all discontinuities.

1)    discontinuous at  

2)    discontinuous at  

3)    discontinuous at  

4)    continuous for all x

Q15
Question 15        4 / 4 points
In an AC circuit, the current has the form  for constants   The power is defined as   for a constant  . Find the average value of the power by integrating over the interval  

Q16
Question 16        4 / 4 points
Is the following differential equation separable or not?

1)    separable
2)    not separable

Q17
Question 17        4 / 4 points
Find the derivative   implicitly.


Q18
Question 18        4 / 4 points
Compute the sum of the form

for the given function and  -values, with  equal to the difference in adjacent  's.

Q19
Question 19        4 / 4 points
An object propelled from the ground with an initial velocity of 50 ft/s will reach a maximum height of 39.1 ft. If the initial velocity is increased 18%, by what percentage will the maximum height increase? Round percentages to the nearest integer.

1)    18%
2)    39%
3)    3%
4)    28%

Q20
Question 20        4 / 4 points
Using the critical numbers of  , use the Second Derivative Test to determine all local extrema.
critical numbers:  ; local max  ; local min  

2)    critical numbers:  ; local max  ; local min  

3)    critical numbers:  ; local max  ; local min  

4)    critical numbers:  ; local max  ; local min  


Q21
Question 21        4 / 4 points
Determine whether the integral converges or diverges. Find the value of the integral if it converges.

1)    converges to 0
2)    converges to  

3)    converges to  

4)    diverges

Q22
Question 22        4 / 4 points
Is the following differential equation separable or not?

1)    separable
2)    not separable

Q23
Question 23        4 / 4 points
Evaluate the integral using integration by parts and substitution (as we recommended in the text, "Try something!").

Q24
Question 24        4 / 4 points
Find the derivative of 

Q25
Question 25        4 / 4 points
Find the limit or explain why it does not exist.

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