Solution for Question No 4.4.1 Introduction to Mathematical Programming

For the Giapetto problem (Example 1 in Chapter 3), show how the basic feasible solutions to the LP in standard form correspond to the extreme points of the feasible region.

STEP-BY-STEP SOLUTION:

• Step 1 of 4
  Consider the following objective function
  
  
  We introduce slack variables
  
  Such that
  
  Therefore, the standard form is
  
• Step 2 of 4
  The feasible region is shown below.
  

  

  From the graph we can see that the feasible region is HEFGD and profit Z will be maximum at the point which is.
• Step 3 of 4
  The extreme points of the feasible region are
  
  Now, the basic feasible solutions are given in the table below.
  

  
• Step 4 of 4
  From the table, we can see that the basic feasible solutions in standard form correspond to the extreme points of the feasible region.

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Corresponding Textbook

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Introduction to Mathematical Programming | 4th Edition

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Solutions for Problems in Chapter 4.4