# Intro to Management Science Ch 4 Solutions

**Topics:**Linear programming, Optimization, Operations research

**Pages:**28 (4744 words)

**Published:**July 9, 2012

Linear Programming Applications in Marketing, Finance and Operations Management

Learning Objectives

1.Learn about applications of linear programming that have been encountered in practice.

2.Develop an appreciation for the diversity of problems that can be modeled as linear programs.

3.Obtain practice and experience in formulating realistic linear programming models.

4.Understand linear programming applications such as:

media selectionproduction scheduling

portfolio selectionwork force assignments

blending problems

Note to Instructor

The application problems of Chapter 4 have been designed to give the student an understanding and appreciation of the broad range of problems that can be approached by linear programming. While the problems are indicative of the many linear programming applications, they have been kept relatively small in order to ease the student's formulation and solution effort. Each problem will give the student an opportunity to practice formulating a linear programming model. However, the solution and the interpretation of the solution will require the use of a software package such as Microsoft Excel's Solver or LINGO.

Solutions:

1.a.LetT = number of television spot advertisements

R = number of radio advertisements

N = number of newspaper advertisements

|Max |100,000T |+ |18,000R |+ |40,000N | | | | |s.t. | | | | | | | | | | | 2,000T |+ | 300R |+ | 600N |≤ |18,200 |Budget | | | T | | | | |≤ |10 |Max TV | | | | | R | | |≤ |20 |Max Radio | | | | | | | N |≤ |10 |Max News | | | -0.5T |+ | 0.5R |- | 0.5N |≤ |0 |Max 50% Radio | | | 0.9T |- | 0.1R |- | 0.1N |≥ |0 |Min 10% TV |

T, R, N, ≥ 0

| | |Budget $ | | |Solution: |T = 4 | $8,000 | | | |R = 14 | 4,200 | | | |N = 10 | 6,000 | | | | |$18,200 |Audience = 1,052,000. |

OPTIMAL SOLUTION

|Optimal Objective Value | | |1052000.00000 | | | | | | | |Variable |Value |Reduced Cost | |T |4.00000 |0.00000 | |R |14.00000 |0.00000 | |N |10.00000 |11826.08695 | | | | | |Constraint |Slack/Surplus |Dual Value | |1 |0.00000 |51.30430 | |2 |6.00000 |0.00000 | |3 |6.00000 |0.00000 | |4...

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