onsider the linear program. Min     7A + 5B     s.t.         2A + 1B ≥ 8   1A + 1B ≥ 8   1B ≤ 3   A, B ≥ 0     (a) Write the problem in standard form. Min     7A  +  5B  +              S1  +              S2  +              S3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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onsider the linear program.
Min     7A + 5B    
s.t.      
  2A + 1B 8
  1A + 1B 8
  1B 3
  A, B ≥ 0    
(a)
Write the problem in standard form.
Min     7A  +  5B  + 
 
 
 
 
 
 
 
S1
 + 
 
 
 
 
 
 
 
S2
 + 
 
 
 
 
 
 
 
S3
   
s.t.                          
  2A  +  1B  + 
 
 
 
         =  8
  1A  +  1B      + 
 
 
 
     =  8
  0A  +  1B          + 
 
 
 
 =  3
A, B, S1, S2, S3       0
(b)
Solve the problem using the graphical solution procedure. What is the value of the objective function?
 
 
 
 at (A, B) = 
 
 
 
 
 
 
 
 
(c)
What are the values of the slack and surplus variables?
S1 =
S2 =
S3 =
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