Question
Asked Nov 14, 2019
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19. Given the linear program
  Max 3A +4B
  s.t.
-1A + 2B< = 8
 1A + 2B< =12
 2A + 1B< =16
       A,B< = 0

d. What is the value of slack variable 1?
e. What is the value of slack variable 2?
f. What is the value of slack variable 3?

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Expert Answer

Step 1

The given LPP is as follows.

Z (A, B) = 3A +4B +0S1+0S2+0S3.

Subject to its constraints,

–1A + 2B + S1 = 8                                                       …… (1)

1A + 2B+         S2=12                                                 …… (2)

2A + 1B              + S3 =16                                          …… (3)

A, B >= 0

Solve L1 and L2 as follows,

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Step 2

Substitute the value of A and B in the given three equat...

-A+2B+S, = 8
20
16
S 8
3
3
28
3
Thus, the value of the slack variable 1 is 28/3.
A+2B S2 12
16
20
S, 12-
3
3
0
Thus, the value of the slack variable 2 is 0.
2A+ B+S 16
40
8
S3 16
3
0
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Image Transcriptionclose

-A+2B+S, = 8 20 16 S 8 3 3 28 3 Thus, the value of the slack variable 1 is 28/3. A+2B S2 12 16 20 S, 12- 3 3 0 Thus, the value of the slack variable 2 is 0. 2A+ B+S 16 40 8 S3 16 3 0

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