# Ohio State University Programming Questions

Description

2 attachmentsSlide 1 of 2attachment_1attachment_1attachment_2attachment_2

Unformatted Attachment Preview

Exercise 1: Alabama Atlantic is a lumber company that has three sources of wood and five
markets to be supplied. The annual availability of wood at sources 1, 2, and 3 is 15, 20, and 15
million board feet, respectively. The amount that can be sold annually at markets 1, 2, 3, 4, and 5
is 11, 12, 9, 10, and 8 million board feet, respectively. In the past the company has shipped the
wood by train. However, because shipping costs have been increasing, the alternative of using
ships to make some of the deliveries is being investigated. This alternative would require the
company to invest in some ships. Except for these investment costs, the shipping costs in thousands
of dollars per million board feet by rail and by water (when feasible) would be the following for
each route:
Unit Cost by Rail (\$1000βs) Market
Unit Cost by Ship (\$1000βs) Market
1
2
3
4
5
1
2
3
4
5
1
61
72
45
55
66
31
38
24

35
2
69
78
60
49
56
36
43
28
24
31
3
59
66
63
61
47

33
36
32
26
Source
The capital investment (in thousands of dollars) in ships required for each million board feet to be
transported annually by ship along each route is given as follows:
Investment for Ships (\$1000βs) Market
Source
1
2
3
4
5
1
275
303
238

285
2
293
318
270
250
265
3

283
275
268
240
Considering the expected useful life of the ships and the time value of money, the equivalent
uniform annual cost of these investments is one-tenth the amount given in the table. The objective
is to determine the overall shipping plan that minimizes the total equivalent uniform annual cost
(including shipping costs).
You are the head of the OR team that has been assigned the task of determining this shipping plan
for each of the following three options.
Option 1: Continue shipping exclusively by rail.
Option 2: Switch to shipping exclusively by water (except where only rail is feasible).
Option 3: Ship by either rail or water, depending on which is less expensive for the route.
Present your results for each option. Compare.
Finally, consider the fact that these results are based on current shipping and investment costs, so
the decision on the option to adopt now should consider managementβs projection of how these
costs are likely to change in the future. For each option, describe a scenario of future cost changes
that would justify adopting that option now.
Exercise 5: Northeastern Airlines is considering the purchase of new long-, medium-, and shortrange jet passenger airplanes. The purchase price would be \$67 million for each long-range plane,
\$50 million for each medium-range plane, and \$35 million for each short-range plane. The board
of directors has authorized a maximum commitment of \$1.5 billion for these purchases. Regardless
of which airplanes are purchased, air travel of all distances is expected to be sufficiently large that
these planes would be utilized at essentially maximum capacity. It is estimated that the net annual
profit (after capital recovery costs are subtracted) would be \$4.2 million per long-range plane, \$3
million per medium-range plane, and \$2.3 million per short-range plane. It is predicted that enough
trained pilots will be available to the company to crew 30 new airplanes. If only short-range planes
were purchased, the maintenance facilities would be able to handle 40 new planes. However, each
1
medium-range plane is equivalent to 1 3 short-range planes, and each long-range plane is
2
equivalent to 1 3 short-range planes in terms of their use of the maintenance facilities. The
information given here was obtained by a preliminary analysis of the problem. A more detailed
analysis will be conducted subsequently. However, using the preceding data as a first
approximation, management wishes to know how many planes of each type should be purchased
to maximize profit.
a. Formulate an IP model for this problem.
b. Use the computer to solve this problem.
c. Solve this problem using the branch-and-bound algorithm (you can use either Excel or
python to help solve LP problems).
Exercise 3: Consider the two-variable integer program:
max 9π₯1 + 5π₯2
subject to
4π₯1 + 9π₯2 β€ 35
π₯1 β€ 6
π₯1 β 3π₯2 β₯ 1
3π₯1 + 2π₯2 β€ 19
π₯1 , π₯2 β πΌ +
Solve by branch-and-bound graphically and algebraically.

attachment

Tags:
programming

IT

AI

User generated content is uploaded by users for the purposes of learning and should be used following Studypool’s honor code & terms of service.

## Reviews, comments, and love from our customers and community

### Article Writing

Great service so far. Keep doing what you do, I am really impressed by the work done.

Researcher

### PowerPoint Presentation

I am speechless…WoW! Thank you so much! Definitely, the writer is talented person. She provided me with an essay a day early before the due date!

#### Stacy V.

Part-time student

### Dissertation & Thesis

This was a very well-written paper. Great work fast. I was in pretty desperate need for help to finish this paper before the due date, which was in nine hours.

Student

### Annotated Bibliography

I love working with this company. You always go above and beyond and exceed my expectations every time. Kate did a WONDERFUL job. I would highly recommend her.

Student

### Book Report / Review

I received my order wayyyyyyy sooner than I expected. Couldn’t ask for more. Very good at communicating & fast at replying. And change & corrections she put in the effort to go back and change it!

Student

### Essay (Any Type)

On time, perfect paper. All concerns & matters I had Tom was able to answer them! I will definitely provide him with more orders!

Student

### Case Study

Awesome! Great papers, and early! Thank you so much once again! Definitely recommend to trust James with your assignments! He won’t disappoint!

#### Kaylin Green

Student

Thank you Dr. Rebecca for editing my essays! She completed my task literally in 3 hours. For sure will work with her again, she is great and follows all instructions

Researcher

### Critical Thinking / Review

Extremely thorough summary, understanding and examples found for social science readings, with edits made as needed and on time. It’s like having a tutoring service available (:

Customer

### Coursework

Perfect!I only paid about \$80, which i think was a good price considering what my paper entailed. My paper was done early and it was well written!

Student