Essentials of Business Analytics (MindTap Course List)
Essentials of Business Analytics (MindTap Course List)
2nd Edition
ISBN: 9781305627734
Author: Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson
Publisher: Cengage Learning
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Chapter 12, Problem 5P

Grave City is considering the relocation of several police substations to obtain better enforcement in high-crime areas. The locations under consideration together with the areas that can be covered from these locations are given in the following table:

Chapter 12, Problem 5P, Grave City is considering the relocation of several police substations to obtain better enforcement

  1. a. Formulate an integer programming model that could be used to find the minimum number of locations necessary to provide coverage to all areas.
  2. b. Solve the problem in part (a).
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a) Give the names of three types of integer programming models and explain them.
The Progressive Company's research and development division is in the process of developing four lines of potential new products. Management must decide which of these four products to manufacture and at what levels. You have asked the OI department to formulate a mathematical programming model to find the most profitable mix of products. The start-up of the manufacture of any product is associated with a substantial cost, which is given in the first line of the table. The management objective is to find the product mix that maximizes total profit (total net income minus fixed costs). Define the continuous decision variables x1, x2, x3, and x4 as the production levels of products 1, 2, 3, and 4. By company policy, management has imposed the following restrictions on these variables:1. At most, only two of these products should be produced.2. Either product 3 or 4 can be produced only if product 1 or 2 is produced.3. Either 5x1 1 3x2 1 6x3 1 4x4 # 6,000 or 4x1 1 6x2 1 3x3 1 5x4 # 6,000.…
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   Formulate the integer programming model for this problem and solve it by using the computer.
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