Please explain

Question 1

Consider the following linear programming problem:

Maximize 3.5x1 + 7x2

Subject to
4x1 + 3x2 > =12

-4x1 - 6x2 =< 12

x2 > =3
x1, x2 > 0

The above linear programming problem:
exhibits unboundedness

Question 2

Consider the following linear programming

Minimize 6x1 + 4x2

Subject to
5x1 + 3x2 =< 15

6x1 + 8x2 > =48

x2 > =6
x1, x2 > 0

The above linear programming problem:

exhibits infeasibility

Warehouse Location - The FMC Corporation*

The FMC Corporation is a large diversified producer of machinery, chemicals, films, and fibers such as nylon. The company has annual sales which place it in the top hundred corporations in the nation. The study presented in this case was done for FMC's Link-Belt Products Division, manufacturers of a broad line of industrial equipment. The study was done by FMC's own consultants, people who are available to work with any of the company's divisions.

A few years before the beginning of this study, Link-Belt management began to feel that perhaps it should reduce the number of warehouses. This feeling was based on several factors, including the decrease in transportation time necessary to reach customers, the lower cost of communication services, higher labor costs, and improvements in techniques of automating warehouses.

The company had warehouses in Philadelphia; Atlanta; Columbus, Ohio; Chicago; Kansas City; Dallas; Reno; Seattle; Houston; and Portland, Oregon. The question presented by the Link-Belt management to the consultants: Should any of the current warehouses be closed, and, in general, what possible configuration of warehouse sites would provide the lowest possible cost while still providing good service to customers?

Dollar amounts reflecting total warehouse sales, tonnages handled, and total operating costs are considered confidential by FMC. However, in the most recent year for which an analysis of figures could be made, the percentage breakdown for Link-Belt's warehouse operating costs were as follows: 19% for freight, 42% for inventory investment, and 39% for operating expenses.

To begin the analysis, 17 additional cities were selected as potential warehouse sites. Since construction and land costs vary from city to city, it was necessary to develop for each city an equation which represented the local costs of construction. In developing this equation, we shall use the following variable.

A = warehouse floor area (in thousands of square feet)
Cc = cost of labor and materials to build a warehouse (in thousands of dollars)
L = amount of land needed for warehouse (in acres)
C1 = cost of land (in thousands of dollars)
I = inventory in a warehouse at a given time (in pounds)
T = total quantity of merchandise going through a warehouse in a year (in thousands of pounds)
For example, if A represents the warehouse area in thousands of square feet, and Cc represents the cost of labor and materials in thousands of dollars, then

Cc = 12.5 + 3.75A
was found to provide a good approximation to the cost for labor and materials in Atlanta, while

Cc = 18.75 + 5.6A
is a similar equation for Chicago. These equations were obtained by studying construction costs in the cities in question.

Land prices also vary from city to city. Again using information obtained about each of the cities in question, it was estimated that the amount of land, L, in acres, needed for a warehouse of area A, in thousands of square feet, is given by

L = 0.875 + 0.0315A.
For Chicago, the cost of this land, C1, in thousands of dollars, is given by A, in thousands of square feet, is given by

C1 = 30.6 + 1.10A,
while the cost equation for Atlanta is

C1 = 14.8 + 0.94A.
Based on past records, the company knows that one square foot of warehouse area can store about 70 pounds of merchandise, or, if I represents inventory measured in pounds in a warehouse at a given time, then

I = 70A.
The inventory at a given time, again from experience, is also given by

I = 180 + 0.1435T,
where T is the total weight of merchandise in thousands of pounds that go through the warehouse in a year.

Using the above equations, we can find the cost of land, labor, and materials for a new warehouse in Chicago in terms of T—that is, we can find the cost in terms of the quantity of merchandise going through the warehouse in a year. To find the cost for labor and materials, we begin with

Cc = 18.75 + 5.6A,
and since I = 70A, or A = I/70, we get

We also know that I = 180 + 0.1435T; thus

which simplifies to

Cc = 33.15 + 0.0115T.
To find the cost of land, go through the same steps to obtain

C1 = 33.47 + 0.00225T
for the equation which gives the cost of land for a warehouse in Chicago.

Using these equations, the analysts prepared the following chart.

Cost of a Warehouse in Chicago   Fixed Cost   Variable cost (dollars per 1000 pounds)
Labor, materials   $33,000   $11.50
Land   $33,500   $2.25
Total   $66,500   $13.75
The numbers in this chart were obtained as follows. We know that the cost of land in Chicago is given by C1 = 33.47 + 0.00225T. The fixed cost is found by letting T = 0: C1 = 33.47 + 0.00225(0) = 33.47, which represents a fixed cost of about $33,500. The variable cost is given by 0.00225 thousands of dollars, which is about $2.25 per thousand pounds of merchandise.

Charts similar to the one above could be made for each of the other cities under discussion. Using all these results, and a process called linear programming, the analysts recommended the following consolidation of warehouse sites. All warehousing should be centralized in five warehouses, located in Philadelphia, Atlanta, Indianapolis, Dallas, and San Francisco. Operating from these five cities will save $600,000 annually, with an additional $730,000 to be realized from selling the warehouses which would be closed. The analysts estimated that service to customers would be as follows: it would be possible to reach eighty-seven percent of the market from these five warehouses in two days or less (compared to current delivery times of one day or less for 89% of all customers), with the remaining 13% reached in three days. About half the market will have delivery times of one day or less.

Exercises

1.  
Complete each of the following steps.

(a)   Cost of labor and materials in Atlanta:
Cc = ____________________.
(b)   Since A = I/70 and I = 180 + 0.01435T, we have

(c)   The equation for the cost of land in Atlanta is
Cl = ______________________________________.
(d)   We have

2.  
Complete the following chart.

Cost of a Warehouse in Atlanta   Fixed Cost   Variable cost
Labor, materials        
Land        
Total        

3.  
Suppose the cost equations for a Sacramento warehouse can be given by

Cc = 11.4 + 4.20A,
C1 = 12.9 + 0.90A.
(a)  
Obtain Cc and C1 in terms of T. (Hint: Go through the steps of Exercise 1 above.)

(b)  
Complete a table, similar to the one of Exercise 2, for a warehouse in Sacramento.

4.  
Show that warehouse area A, in thousands of square feet, needed for a certain annual total quantity of goods, T, in thousands of pounds, is given by

    A = 2.57 + 0.00205T,     
or   T = 487A - 1250.

Find the solution to the boundary value problem:

?^2?/??2−6??/??+5?=0,   ?(0)=10,?(1)=6

Please show me all your work, I want to know where I went wrong. Thank you!

Cheetah Copy purchased a new copy machine. The new machine cost $136,000 including installation. The company estimates the equipment will have a residual value of $34,000. Cheetah Copy also estimates it will use the machine for four years or about 8,000 total hours. Actual use per year was as follows:

2. Prepare a depreciation schedule for four years using the double-declining-balance method.

Many Wall Street firms use LP models to select a
desirable bond portfolio. The following is a simplified
version of such a model. Solodrex is considering
investing in four bonds; $1 million is available for
investment. The expected annual return, the worst-case
annual return on each bond, and the duration of each
bond are given in the file P04_56.xlsx. (The duration
of a bond is a measure of the bond’s sensitivity
to interest rates.) Solodrex wants to maximize
the expected return from its bond investments,
subject to three constraints:
■ The worst-case return of the bond portfolio must
be at least 7%.
■ The average duration of the portfolio must be
at most 6.5. For example, a portfolio that invests
$600,000 in bond 1 and $400,000 in bond
4 has an average duration of [600,000(3) 1
400,000(9)]Y1,000,000 5 5.4.
■ Because of diversification requirements, at most
40% of the total amount invested can be invested in
a single bond.
Determine how Solodrex can maximize the expected
return on its investment.

thanks a lot !!!

Collin and Devonte plan to send their son to university. To pay for this they will contribute equal monthly payments to an account bearing interest at an annual rate of 6.7%, compounded monthly. They will make these payments for 12 years.  Five years after their last contribution, they will begin the first of 60 monthly withdrawals of $3,830 to pay the university's installment bills. How large must their monthly contributions be?

Several factors are involved in the creation of a confidence interval. Among them are the sample​ size, the level of​ confidence, and the margin of error. Which statements are​ true?

Select all true statements below.

A.

For a certain confidence​ level, you can get a smaller margin of error by selecting a bigger sample.

B.

For a given sample​ size, reducing the margin of error will mean lower confidence.

C.

For a given confidence​ level, a sample 9 times as large will make a margin of error one third as big.

D.

For a fixed margin of​ error, smaller samples will mean lower confidence.

E.

None of these statements are true.

Find the least positive solution of (a) x^2 − 29y^2 = −1 (b)x^2 − 29y^2 = 1

In a small town there are two places to eat: 1) a Chinese restaurant and 2) a pizza place. Everyone in town eats dinner at one of the these two places or eats dinner at home.

Assume the 20% of those who eat in the Chinese restaurant go to the pizza place the next time and 40% eat at home. From those who eat at the pizza place, 50% go to the Chinese restaurant and 30% eat at home the next time.  From those who eat at home, 20% go to the Chinese restaurant and 40% to the pizza place next time. We call this situation a system. This system can be modeled as a discrete-time Markov chainwith three states.

1. Define the three states and write down the one-step transition probability matrix.
2. If a family has decided to eat dinner in the Chinese restaurant with the probability of 0.05 or in the pizza place with the probability of 0.15 today, what is the probability that this family will eat dinner at home in two days
3. If a lady is having pizza today, how long will it take for her to have pizza again
4. Given that a man has been eating at the Chinese restaurant today and yesterday, on average, how long will it take for him to eat at the pizza place for the first time?
5. If a family plans to eat at home on Sunday, what is the probability that they will eat Chinese on Tuesday (same week) for the first timethen they will eat Pizza on Friday (same week) for the first time?

Discussion

Let us assume this gift shop volume is growing, therefore, you have a decision to make:

• Should I corporate the company?
• Should I begin a chain stores?
• Should I a part of franchise company?
• Or, Should I stay an incorporate company?

Write a brief description of the above options. What option do you prefer your store to follow?

Your discussion should be minimum 400 words.

Find the symmetric image of P(−28,18,20) about the plane passing through Q(0,0,0) and perpendicular to the vector n=[−5,5,2].

1. Suppose the equilibrium price for an average hospital stay in the absence of insurance is $10,000. At that price, 1000 people are hospitalized each year. Now suppose an insurer offers a policy to lower the out of pocket price of a stay to $100, and at that price, 1200 people are hospitalized.

a) How much TOTAL premium revenue must be collected to finance this arrangement?

b) How much premium revenue per hospitalized person must be collected? Would the average person be willing to pay this premium if they were risk averse?

c) Now suppose there are 120,000 people near this hospital, all of whom think they have an equal chance (1%) of being hospitalized. What must the per person premium be now?

Binary Tree

Create a binary search tree using the given numbers in the order they’re

presented. State if the resulting tree is FULL and/or BALANCED.

37, 20, 18, 56, 40, 42, 12, 5, 6, 77, 20, 54

Please follow the comment and solve question 6 and question 7 if you want to get thumbs up. Thank you.

6- Let xn ≥0 for all n∈N.

6-1) If xn →0, show that√xn →0.

6-2) If xn →x, show that√xn →√x.

Let A = lim n→∞an. Use an+1 =√2+an, the result of Exercise 6 and limit laws to prove that A = 2.

he market demand function for corn is

              Q^d = 25 - 2P The market supply function is

                Q^s = 5P -3

both measured in billions of bushels per year. What would be the welfare effects of a policy that put a cap of $3.50 per bushel on the price farmers can charge for corn? (Assume that corn is purchased by the consumers who place the highest value on it.)

Instructions: Round quantities to one decimal place. Round prices and surpluses to two decimal places.