Numerical Analysis Using MATLAB and Spreadsheets
This concise text provides complete, clear, and detailed explanations of the principal numerical analysis methods and well known functions used in science and engineering.
TABLE OF CONTENTS Numerical Analysis Using MATLAB and Spreadsheets
Chapter 16: Optimization Methods
This chapter introduces three methods for maximizing or minimizing some function in order to achieve the optimum solution. These methods are topics discussed in detail in a branch of mathematics called operations research that is concerned with financial and engineering economic problems. Our intent here is to introduce these methods with the basic ideas. We will discuss linear programming, dynamic programming, and network analysis and we will illustrate these with some simple but practical examples.
16.1 Linear Programming
In linear [*] programming we seek to maximize or minimize a particular quantity, referred to as the objective, which is dependent on a finite number of variables. These variables may or may not be independent of each another, and in most cases are subject to certain conditions or limitations referred to as constraints.
Example 16.1
The ABC Semiconductor Corporation produces microprocessors ( ? Ps) and memory ( RAM) chips. The material types, A and B, required to manufacture the ? Ps and RAMs and the profits for each are shown in Table 16.1.
| Parts of Material Types | ||
|---|---|---|
| ? Ps | RAMs(1000s) | |
| Semiconductor Material A | 3 | 2 |
| Semiconductor Material B | 5 | 10 |
| Profit | $25.00 per unit | $20.00 per 1000 |
Due to limited supplies of silicon, phosphorus and boron, its product mix at times of high consumer demand, is subject to limited supplies. Thus, ABC Semiconductor can only buy 450 parts of Material A,...
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