# Which supplier should Tri-County contract with to supply the additional capacity?

Tri-County Utilities, Inc. supplies natural gas to customers in three-county area. The company purchases purchases natiural gas from two companies: Southern Gas and Northwest Gas. Deman forecasts for the coming winter season are as follows: Hamilton County, 400 units; Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quanities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars) are as follows:
To
From Hamilton Butler Clermont
Southern Gas 10 20 15
Northwest Gas 12 15 18
a. Develop a network representation of this problem.
b. Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs.
c. Describe the distribution plan and show the total distribution cost.
d. Recent residential and industrial growth in Butler County has the potential for increasing demand by as much as 100 units. Which supplier should Tri-County contract with to supply the additional capacity?

5. Premier Consulting’s two consultants. Avery and Baker, can be scheduled to work for clients up to a maximum of 160 hours each over the next four weeks. A third consultant, Campbell, has some administrative assignments already planned and is available for clients with projects in process. The estimated hourly requirements for each of the clients over the four-week period as follows:

Client Hours
A 180
B 75
C 100
D 85

Hourly rates vary for the consultant-client combination and are based on several factors, including project type and the consultant’s experience. The rates (dollars per hour) for each consultant-client combination are as follows:

Client
Consultant A B C D
Avery 100 125 115 100
Baker 120 135 115 120
Campbell 155 150 140 130

a. Develop a network representation of the problem.
b. Formulate the problem as a linear program, with the optimal solution providing the hours each consultant should be scheduled for each client to maximize the consulting firm’s billings. What is the schedule and what is the total billing?
c. New information shows that Avery doesn’t have the experience to be scheduled for client B. If this consulting assignment is not permitted, what impact does it have on total billings? What is the revised schedule?

7. Aggie Power Generation supplies electrical power to residential customers for many U.S. cities. Its main power generation plants are located in Los Angeles, Tulsa, and Seattle. The following table shows Aggie Power Generation’s major residential markets, the annual demand in each market (in megawatts or MWs) and the cost to supply electricity to each market from each power generation plant (prices are in \$/MW).

Distribution Costs
City Los Angeles Tulsa Seattle Demand (MWs)
Seattle \$356.25 \$593.75 \$59.38 950.00
Portland \$356.25 \$593.75 \$178.13 831.25
San Francisco \$178.13 \$475.00 \$296.88 2375.00
Boise \$356.25 \$475.00 \$296.88 593.75
Reno \$237.50 \$475.00 \$356.25 950.00
Bozeman \$415.63 \$415.63 \$296.88 593.75
Laramie \$356.25 \$415.63 \$356.25 1187.50
Park City \$356.25 \$356.25 \$475.00 712.50
Flagstaff \$178.13 \$475.00 \$593.75 1187.50
Durango \$356.25 \$296.88 \$593.75 1543.75

7b. If at most 4000 MWs of power can be supplied by any one of the power plants, what is the optimal solution? What is the annual increase in power distribution cost that results from adding these constraints to the original formulation?

9. The Ace Manufacturing Company has orders for three similar products:
Orders
Product (units)
A 2000
B 500
C 1200

Three machines are available for the manufacturing operations. All three machines can be produce all the products at the same products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are as follows:
Product
Capacity
Machine (units) Machine A B C
1 1500 1 \$1.00 \$1.20 \$0.90
2 1500 2 \$1.30 \$1.40 \$1.20
3 1000 3 \$1.10 \$1.00 \$1.20

Use the transportation model to develop the minimum cost production schedule for the products and machines. Show the linear programming formulation.

19. A local television station plans to drop four Friday evening programs at the end of the season. Steve Botuchis, the station manager, developed a list of six potential replacement programs. Estimates of the advertising revenue (\$) that can be expected for each of the new programs in the four vacated time slots are as follows. Mr. Botuchis asked you to find the assignment of programs to time slots that will maximize total advertising revenue.

5:00- 5:30- 7:00- 8:00-
5:30 PM. 6:00 PM. 7:30 PM. 8:30 PM.
Home Improvement 5000 3000 6000 4000
World News 7500 8000 7000 5500
NASCAR Live 8500 5000 6500 8000
Wall Street Today 7000 6000 6500 5000
Holiday Briefings 7000 8000 3000 6000
Ramundo & Son 6000 4000 4500 7000

a. Develop a network representation of the problem.

Pages (550 words)
Approximate price: -

Why Homework Market

Quality Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

Qualified Writers

We have hired a team of professional writers experienced in academic and business writing. Most of them are native speakers and PhD holders able to take care of any assignment you need help with.

Unlimited Revision

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account.

Timely Delivery

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. We will always strive to deliver on time.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text.

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

## Calculate the price of your order

Total price:
\$0.00

How it works?

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Homework Market Writing Services

No need to work on essay at night. Sleep tight, we will cover your back. We offer all kinds of essay writing services.

## Essay Writing Services

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.