On August 27, 2012 the U.S. federal rate* was 0.25% per annum and Japan’s interbank rate was 0.2% per annum. Other things being equal calculate the interest rate parity 90-day forward rate of the yen/dollar.

On August 27, 2012 the U.S. federal rate* was 0.25% per annum and Japan’s interbank rate was 0.2% per annum. Other things being equal calculate the interest rate parity 90-day forward rate of the yen/dollar. Formulate and then solve a linear programming model of this problem, to determine how many containers of each product to produce tomorrow to maximize profits.

Formulate and then solve a linear programming model of this problem, to determine how many containers of each product to produce tomorrow to maximize profits. The company makes four juice products using orange, grapefruit, and pineapple juice.

Product Retail Price per Quart
Orange juice \$1.00
Grapefruit juice .90
Pineapple juice .80
All-in-One 1.10 If the point (2,5) is shifted 3 units to the right and 2 units down in the X-Y plane, what are its new coordinates?

Module 1 – SLP
Linear Expressions
Exercises

Let’s continue to look at formulas.
1. If the point (2,5) is shifted 3 units to the right and 2 units down in the X-Y plane, what are its new coordinates?
2. If the point (-1,6) is shifted 2 units to the left and 4 units up, what are its new coordinates.
3. Find all the points having an x-coordinate of 3 whose distance from the point (-2, -1) is 13.
4. Find all the points having a y-coordinate of -6 whose distance is from the point (1,2) is 17.
5. Find all points on the y-axis that are 6 units from the point (4, -3). Maximize Z = 2×1 + 10×2 Subject to Problem 19-1B

Maximize Z = 2×1 + 10×2
Subject to
Problem 19-1B

Durability 7×1 + 4×2 ≥ 31 wk
Strength 1×1 + 6×2 ≥ 24 psi
Time 1×1 + 2×2 ≤ 11 hr
x1, x2 ≥ 0

1. What are the optimal values of the decision variables and Z? (Round your answers to 2 decimal places.)

Decision Variables
x1 x2 Z
Optimal values Solve these problems using graphical linear programming and answer the questions that follow. Use simultaneous equations to determine the optimal values of the decision variables.

Solve these problems using graphical linear programming and answer the questions that follow. Use simultaneous equations to determine the optimal values of the decision variables.

a. Maximize Z = 4×1 + 3×2
Subject to

Material 7×1 + 3×2 ≤ 26 lb
Labor 2×1 + 4×2 ≤ 22 hr
x1, x2 ≥ 0

1. What are the optimal values of the decision variables and Z? (Round your answers to 2 decimal places.)

Decision Variables
x1 x2 Z
Optimal values What are the optimal values of the decision variables and Z?

Subject to

Material 20A + 6B ≤ 510 lb
Machinery 25A + 20B ≤ 850 hr
Labor 20A + 30B ≤ 1,000 hr
A , B ≥ 0

1. What are the optimal values of the decision variables and Z?

Decision Variables
A B Z
Optimal values MICO’s CEO knows that you are taking Decision analysis course and he asked you to consider all the alternatives to draw Decision tree and show all EMV’s on tree (show the calculation of EMV’s)?”

MICO Manufacturing Company currently manufacture specific items used in construction. Currently there existing plant is Diesel Base and 90% of time plant is in operation while 10% of time they have to shut down for maintenance.. When plant is in-operation 75% chances that they can earn revenue as high as \$160m. While 20% chances that they can earn revenue as low as \$98m. In Non-operational period of time (when plant is shut down for maintenance) they bear loss of \$29m.

In recent meeting Jeff, proposed following alternatives
Improve the existing plant, develop Natural Gas Model, develop Electrical Model.

Improve existing plant
It requires \$15m to improve/upgrade and they can earn revenue as high as \$182m with 75% chances, and as low as \$102m with 25% chances.

Natural Gas Model (NG)
MICO Engineers will work on New NG model. It requires \$20m and chances for success are only 72%. If NG Model developed successfully, MICO is expecting revenue of \$198m with 47% chances, revenue of \$172m with 30% chances and 23% chances of earning revenue as low as \$155m by using its own distribution channel.

In case of failure they can either stop further progress or give contract to ABC company to develop NG model for them, who offered them to design NG model as per there requirements. ABC will charge \$30m only in case of success. Chances for success are 97%. If ABC fails MICO has to abandon the development of NG model.

In case of success through ABC Company, MICO can use its own distribution channel or they may use ABC distribution channel. In case of the use of ABC distribution channel MICO can earn revenue as high as \$188m with 82% chances and as low as \$157m with 18% chances.

Electrical Model (EM)
They have design of three Electrical models EM-A, EM-B an EM-C.
MICO Engineers will go first for EM-A it requires \$18m and success rate is only 45%. In case of EM-A failure they can either stop the project at this stage or further proceed for EM-B which requires additional \$8m and success rate is 50%. In case of EM-B failure they can either stop the project at this stage or further proceed for EM-C which requires additional \$5m and failure rate is only 12%. In case of EM-C failure MICO has to abandon the development of EM model. (In case of success they will not work on other design/s)

In case of success of
EM-A: they estimated revenue of \$180m with 75% chances and \$162m with 25% chances.
EM-B: they estimated revenue of \$178m with 80% chances and \$148m with 20% chances.
EM-C: they estimated revenue of \$190m with 78% chances, \$170 with 12% chances and \$142 with 10% chances.

MICO’s CEO knows that you are taking Decision analysis course and he asked you to consider all the alternatives to draw Decision tree and show all EMV’s on tree (show the calculation of EMV’s)?” Find Johns expected income and utility. Use this to deduce the risk premium that John is willing to pay to avoid salary uncertainty in his current job.

John works in acompany which is restructuring. He facess three possibilties:with probability 1/2, he will be promoted to a better playingjob and earn 81.With probability 1/4,he will keep his present job, which pays 36.And with probability 1/4.he will be fired,and get unemployment benefits of 16.

john’s utility functions is U(x)=2x (u(x)=two times the square root f(x).
find Johns expected income and utility. Use this to deduce the risk premium that John is willing to pay to avoid salary uncertainty in his current job. If you had two variables and three constraint equations, would you solve this problem using the graphical solution method or the Simplex method?

If you had two variables and three constraint equations, would you solve this problem using the graphical solution method or the Simplex method? The random variable X is Weibull if it has the distribution function

The random variable X is Weibull if it has the distribution function

F(x) = 1 – e-αx

where α > 0 and β > 0 are parameters. Differentiating, we see that the corresponding density function is

f(x) = αβxβ-1e-αx

(Note that if β = 1, then we are actually talking about an exponential random variable.)

(a) Suppose two independent random variables X1 and X2 are Weibull with the same parameters α and β.

(i) What is the density function for Y = max {X1, X2}?

(ii) What is the density function for Z = min {X1, X2}?

(b) The hazard function H associated with a positive random variable X with distribution F and density f is
defined as

H(x) = – log(1 – F(x)),

and the hazard rate is

r(x) =

β

,

x ≥ 0,

β

x≥0

,

(i) Derive an expression for the hazard rate function of X when it is Weibull with parameters α and β.

(ii) What is the hazard rate function when X is exponential with mean 1/α?

(Hint: It may be easier in both (a) and (b) to reason about generic positive random variables with
distribution F and density f, rather than to get bogged down in details related to the Weibull distribution.
Also, recall that the derivative of a function g is

g’(x) =

Finally, think about why r(x) is called a “hazard rate” function.) Cars arrive at the beginning of a long road, starting at time t = 0, with up to one car arriving

Cars arrive at the beginning of a long road, starting at time t = 0, with up to one car arriving every 1
second, independently with probability p per second. Each car has a fixed velocity V > 0 (mph), which is
random and independent from car to car and also independent of the time at which the car arrives. Cars
can overtake each other freely. Let N90 denote the number of cars on the first mile of the road at time t =

90 seconds?

(a) What is the expected value of N90?

(b) Characterize N90 as best you can. Does it have the pmf of one of the random variables discussed in
class? If so, which one?

Suppose that cars arrive according to a Poisson process with rate p (cars/second).
(c) What is the expected value of N90?

(d) What is the pmf of N90? A woman is trapped in a mine having two doors. If she takes the left door, then she will wander around

A woman is trapped in a mine having two doors. If she takes the left door, then she will wander around
and return to the same position after 3 hours. If she takes the right door, the probability that she will be
free after 4 hours, is 1/3; the probability that she will return to the same position after 2 hours is 2/3. In the
first attempt, she picks a door at random (uniformly). However, if she takes one door and returns, she will
try the other door the next time. She restricts attention to just the left and right doors, and never considers
go back the way she came. After her first choice, upon returning, she will alternate doors.

(a) Model the process as a Markov Chain, that is draw a diagram of the Markov Chains indicating the
states and the transition probabilities.

(b) What is the expected duration before she reaches freedom?

(c) What is the expected number of doors she tries before reaching freedom?

(d) Classify each state as transient or recurrent. How many recurrent classes are there? Do steady state
probabilities exist? You are lost in the National Park of Bandrika. Tourists (which look just like Bandrikans) comprise two-

You are lost in the National Park of Bandrika. Tourists (which look just like Bandrikans) comprise two-
thirds of the visitors to the park, and give a correct answer to requests for directions with probability 3/4.
(Answers to repeated questions are independent, even if the question and the person are the same.) If

(a) You ask a passerby whether the exit from the Park is East or West. The answer is “East”. What is the
probability that this is correct?

(b) You ask the same person again, and receive the same reply. What is the probability of being correct?

(c) You ask the same person for the third time, and receive the same reply. What is the probability of
being correct?

(d) You ask for the fourth time, and receive the same reply. What is the probability of being correct?

(f) Contrast your answers in part d and part e and explain. (25pts) Suppose there are five people – 1,2,3,4 and 5 – who rank projects A,B,C and D as follows:

(25pts) Suppose there are five people – 1,2,3,4 and 5 – who rank projects A,B,C and D as
follows:
1
2
3
4
5
A
A
D
C
B
D
C
B
B
C
C
B
C
D
D
B
D
A
A
A

a) (5pts) First consider a pairwise majority vote rule. Will any project be chosen by a majority
vote rule? If so, which one will be chosen and how does it get to be chosen? If not, explain why.
b) (5pts) Then consider a simple plurality voting, under which each voter is allowed to vote for
only one candidate, people are ranked based on the number of votes they get. Will any project
be chosen? If so, which one will be chosen and how does it get to be chosen? If not, explain
why.
c) (5pts) Among the five criteria in Arrow’s Impossibility theorem, which criterion (criteria) does
plurality voting violate? Which criterion (criteria) does plurality voting obey? Explain why it
violates or obeys certain criterion (criteria).
Now
Change the
preferences
of the
previous 5
voters just a
bit: 1
2
3
4
5
A
A
D
C
B
D
C
B
B
D
C
B
C
D
C
B
D
A
A
A

d) (5pts) Again consider a pairwise majority vote rule. Will any project be chosen? If so, which
one will be chosen and how does it get to be chosen? If not, explain why.
e) (5pts) Sketch the preferences of the 5 voters before change and after change? Do multi-
peaked preferences necessarily lead to voting inconsistencies? Describe the techniques employed when showing quantitative differences between Bar and Column chart.

Describe the techniques employed when showing quantitative differences between Bar and Column chart? What is an exponential distribution?

What is an exponential distribution? What is it used for? Provide some examples Are the corner points always the solution to a linear programming problem?

Are the corner points always the solution to a linear programming problem? 1. In a classic study of infant attachment, Harlow (1959) placed infant monkeys in cages with two artificial surrogate mothers. One “mother” was made from bare wire mesh and contained a baby bottle from which the infants could feed.

1. In a classic study of infant attachment, Harlow (1959) placed infant monkeys in cages with two artificial surrogate mothers. One “mother” was made from bare wire mesh and contained a baby bottle from which the infants could feed. The other mother was made from soft terry cloth and did not provide any access to food. Harlow observed the infant monkeys and recorded how much time per day was spent with each mother. In a typical day, the infants spent a total of 18 hours clinging to one of the two mothers. If there were no preference between the two, you would expect the time to be divided evenly, with an average of μ = 9 hours for each of the mothers. However, the typical monkey spent around 15 hours per day with the terry cloth mother indicating a strong preference for the soft, cuddly mother. Suppose a sample of n = 9 infant monkeys averaged M = 15.3 hours per day with SS = 216 with the terry cloth mother. Is this result sufficient to conclude that the monkeys spent significantly more time with the softer mother than would be expected if there were no preference? Use a two-tailed test with α = .05

2. A research would like to examine the effects of humidity on eating behavior. It is known that laboratory rats normally eat an average of µ = 21 grams of food each day. The research selects a random sample of n = 16 rats and places them in a controlled atmosphere room in which the relative humidity is maintained at 90%. The daily food consumption scores for rats are as follows:
14, 18, 21, 15, 18, 18, 21, 18
16, 20, 17, 19, 20, 17, 17, 19
a. Can the researcher conclude that humidity has a significant effect on eating behavior? Use a two-tail test with α = .05.
b. Compute the estimated Cohen’s d and r2 to measure the size of the treatment effect. A company will be able to obtain a quantity discount on component parts for its three products, X1, X2 and X3 if it produces beyond certain limits. To get the X1 discount it must produce more than 50 X1’s. It must produce more than 60 X2’s for the X2 discount and 70 X3’s for the X3 discount. Which of the following pair of constraints enforces the quantity discount relationship on X3?

A company will be able to obtain a quantity discount on component parts for its three products, X1, X2 and X3 if it produces beyond certain limits. To get the X1 discount it must produce more than 50 X1’s. It must produce more than 60 X2’s for the X2 discount and 70 X3’s for the X3 discount. Which of the following pair of constraints enforces the quantity discount relationship on X3?
a. X31  M3Y3 , X32  50Y3
b. X31  M3Y3 , X31  50
c. X32  (1/50)X31 , X31  50
d. X32  M3Y3 , X31  50Y3 The optimal relaxed solution for an ILP has X1 = 3.6 and X2 = 2.9. If we branch on X1, what constraints must be added to the two resulting LP problems?

The optimal relaxed solution for an ILP has X1 = 3.6 and X2 = 2.9. If we branch on X1, what constraints must be added to the two resulting LP problems?
a. X1  3, X1  4
b. X1 = 4
c. 3  X1, X1  4
d. X1  3, X1  4

PLEASE SEE ATTACHED. THIS IS COMING FROM THE AMU COURSE, OPERATIONS RESEARCH W/ SELF TITLED BOOK BY CLIFF RAGSDALE. Does the linear programming approach apply the same way in different applications? Explain why or why not using examples.

Does the linear programming approach apply the same way in different applications? Explain why or why not using examples. Explain how the applications of Integer programming differ from those of linear programming. Why is “rounding-down” an LP solution a suboptimal way to solve Integer programming problems?

Explain how the applications of Integer programming differ from those of linear programming. Why is “rounding-down” an LP solution a suboptimal way to solve Integer programming problems? Sales tax is never rounded to nearest cent. A.)True B.)False

Sales tax is never rounded to nearest cent.
A.)True
B.)False Explain how a multiple optimal solution is recognized when using the simplex algorithm.

Explain how a multiple optimal solution is recognized when using the simplex algorithm. The Webster National Bank is reviewing its service charge and interest-paying policies on checking accounts. The bank has found that the average daily balance on personal checking accounts is \$550, with a standard deviation of \$150.

The Webster National Bank is reviewing its service charge and interest-paying
policies on checking accounts. The bank has found that the average daily balance on
personal checking accounts is \$550, with a standard deviation of
the average daily balances have been found to be normally distributed (Gaussian).

(a) What percentage of personal checking account customers carry average daily
balances in excess of \$800?
(b) What percentage of the bank’s customers carries average daily balances below
of \$200?
(c) What percentage of the bank’s customers carries average daily balances
between \$300 and \$700?
(d) The bank is considering paying interest to customers carrying average daily
balances in excess of a certain amount. If the bank does not want to pay
interest to more than 5% of its customers, what is the minimum average daily
balance it should be willing to pay interest on?
question – 2
A company that manufuture tooth paste is suding What year is it in Japan right now. This is a Math question and I believe it has something to do with with change in Calendar systems and the fact Japan drops a month. The only problem I have is I can no good enough information to know what I should and should not add to find out what year it is in Japan right now.

What year is it in Japan right now. This is a Math question and I believe it has something to do with with change in Calendar systems and the fact Japan drops a month. The only problem I have is I can no good enough information to know what I should and should not add to find out what year it is in Japan right now. which would be an example of data be modeled That Could by a logistic function and Explain why.

which would be an example of data be modeled That Could by a logistic function and Explain why. Explain the concept of simple-complex dimension. 250 words or more and references

Explain the concept of simple-complex dimension. 250 words or more and references In your own words, explain how you determine if a radical is simplified. Using a radical that is not a square root, demonstrate (and explain!) the steps in simplifying that radical completely, including in your explanation a description of when the radical cannot be simplified further. Your radical example must be constructed in such a manner that the original radical can (to some extent!) be simplified!  