Formulate the integer programming model

Reference no: EM13745412

Question 1. The Livewright Medical Supplies Company has a total of 12 salespeople it wants to assign to three regions - the South, the East, and the Midwest. A salesperson in the South earns $600 in profit per month of the company, a salesperson in the East earns $540, and a salesperson in the Midwest earns $375. The southern region can have a maximum assignment of 5 salespeople. The company has a total of $750 per day available for expenses for all 12 salespeople. A salesperson in the South has average expenses of $80 per day, a salesperson in the East has average expenses of $70 per day, and a salesperson in the Midwest has average daily expenses of $50. The company wants to determine the number of salespeople to assign to each region to maximize profit.

a. Formulate an integer programming model for this problem

b. Solve this model by using the computer.

Question 2. Solve the following mixed integer linear programming model by using the computer:

Maximize Z = 5x₁ + 6x₂ + 4x₃

Subject to

5x₁ + 3x₂ + 6x₃ ≤ 20

x₁ + 3x₂ ≤ 12

x1, x₃ ≥ 0

x₂ ≥ 0 and integer

Question 3. The Texas Consolidated Electronics Company is contemplating a research and development program encompassing eight research projects. The company is constrained from embarking on all projects by the number of available management scientists (40) and the budget available for R&D projects ($300,000). Further, if project 2 is selected, project 5 must also be selected (but not vice versa). Following are the resource requirements and the estimated profit for each project.

Project	Expense ($1,000s)	Management Scientists required	Estimated Profit (1,000,000s)
1	$ 60	7	$0.36
2	110	9	0.82
3	53	8	0.29
4	47	4	0.16
5	92	7	0.56
6	85	6	0.61
7	73	8	0.48
8	65	5	0.41

Formulate the integer programming model for this problem and solve it using the computer.

Question 4. During the war with Iraq in 1991, the Terraco Motor Company produced a lightweight, all- terrain vehicle code-named "J99-Terra" for the military. The company is now planning to sell the Terra to the public. It has five plants that manufacture the vehicle and four regional distribution centers. The company is unsure of public demand for the Terra, so it is considering reducing its fixed operating costs by closing one or more plants, even though it would incur an increase in transportation costs. The relevant costs for the problem are provided in the following table. The transportation costs are per thousand vehicles shipped; for example, the cost of shipping 1,000 vehicles from plant 1 to warehouse C is $32,000.

From Plant	Transportation Costs ($1000s) to Warehouse				Annual Production Capacity	Annual Fixed Operating Costs
From Plant	A	B	C	D	Annual Production Capacity	Annual Fixed Operating Costs
1	$56	$21	$32	$65	12,000	$2,100,000
2	18	46	7	35	18,000	850,000
3	12	71	41	52	14,000	1,800,000
4	30	24	61	28	10,000	1,100,000
5	45	50	26	31	16,000	900,000
Annual Demand	6,000	14,000	8,000	10,000

Formulate and solve an integer programming model for this problem to assist the company in determining which plants should remain open and which should be closed and the number of vehicles that should be shipped from each plan to each warehouse to minimize total cost.

Reference no: EM13745412

Questions Cloud

Why is the krebs cycle so important for our bodies : Explain the Krebs cycle process. Why is the Krebs cycle so important for our bodies? Why do many body builders study this process

What were origins of the industrial revolution in britain : Little is known about Toussaint L' Overture. What was unique about his life? What were the origins of the Industrial Revolution in Britain? How did these origins develop between 1780 and 1850?

How were the men convicted of the crime : A man and his wife were on vacation in Paris. On the way back to the hotel, they were approached by two men with weapons who demanded their jewelry. How were the men convicted of the crime

What was impact of urban growth on cities and social classe : How did nationalism and socialism shape European politics in the decades before the Great War? What was the impact of urban growth on cities, social classes, families, and ideas?

Formulate the integer programming model : Formulate an integer programming model for problem - mixed integer linear programming model - Formulate the integer programming model for this problem and solve it using the computer.

Discovery of dna as our hereditary material : Describe the major experiments and scientists involved in the discovery of DNA as our hereditary material and its structure

What were the most significant changes in africa : What were the most significant changes in Africa during the nineteenth century, and why did they occur? What were the causes and consequences of the European empire building after 1880?

Determine what needs the stakeholders for bjb''s products : Determine what needs the stakeholders may have for BJB's products. Analyze the product and needs of BJB, and then select the quality management approach that would be the best fit. Explain your rationale.

Describe levis experience at auschwitz : Describe Levi's experience at Auschwitz. How did camp prisoners treat each other? Why? What does Levi mean by the "gray zone"? How is this concept central to his thinking?

User Account

All Pages