Comment: Need to write a 2-3 page paper, thats it. Don't have to solve problems
Determine the best model type(s) for each(linear, nonlinear, or integer), and then building the model(s) to meet the needs of the scenarios. Given the real-world scenarios, write the appropriate model formulation. DO NOT SOLVE. Write a Word document describing the selections for the appropriate type of model for the three problems. Write the mathematical formulation but do not solve. The paper should be 2 to 3 pages in length.
1. An electronics manufacturing company is planning a research and development program to handle a planned sequence of eight projects. The total budget available for the projects is $350,000. In addition, the company plans to hire 30 engineers for the entire program. If project 2 is selected, then project 7 should also be selected (but not vice versa). The anticipated profits and the resources needed for each project are shown in Table 1.Formulate a programming problem to determine the individual projects that the company should select in order to maximize its total profit.
|
Project
|
Project Estimated Profit
|
Project Expense
|
Engineers Required
|
|
1
|
$290,000
|
$53,000
|
6
|
|
2
|
$510,000
|
$47,000
|
7
|
|
3
|
$340,000
|
$28,000
|
4
|
|
4
|
$160,000
|
$17,000
|
4
|
|
5
|
$560,000
|
$56,000
|
8
|
|
6
|
$410,000
|
$22,000
|
5
|
|
7
|
$340,000
|
$37,000
|
4
|
|
8
|
$560,000
|
$42,000
|
6
|
Table 1: Details for Each project
2. In a metropolitan area, 45,000 people want to travel from the city suburbs to the city center. To do so, they can drive, take a city bus, or use the subway system. If x1number of people drive and x2 number of people take a bus, it will take respectively (0.0006x1+30) and (0.0003x2+40) minutes to make the trip; whereas a subway trip is expected to take 45 minutes. The city bus system can transport a maximum of 20,000 people to the city center, while the subway system has a capacity of transporting at most 10,000. Write a programming formulation that minimizes the average travel time for each person
3. A company that sells computer network systems is planning to offer free memory storage services to its customers where picture, music, and video files can be stored. The company is planning to initially start with three servers each of whose capacity is provided in Table 2
Time (In seconds)
|
Server
|
Picture
|
Music
|
Video
|
|
1
|
1
|
2
|
7
|
|
2
|
3
|
4
|
8
|
|
3
|
5
|
6
|
10
|