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The feasible region is bounded by line segments that
consecutively connect extreme points (0, 0), (0, 4), (3,
5), (8, 0) and (0, 0). [Note that (0, 0) is listed twice to
"finish the circuit."]
SAME AS PREVIOUS EMAIL
b
(0, 0): s1 and s2 are basic, x1 and x2 are nonbasic.
(0, 4): x2 and s2 are basic, x1 and s1 are nonbasic.
(3, 5): x1 and x2 are basic, s1 and s2 are nonbasic.
(8, 0): x1 and s1 are basic, x2 and s2 are nonbasic.
SAME AS FIRST WORKING OF #4.
c
The values that minimize z = 5x1 + x2 are the values that
maximize
y = 5x1  x2. *** y =  z ***
THIS TIME: use x1 and s1 for nonbasic variables
3x2 = 12 + x1  s1
x2 + s2 = 8  x1
y + x2 = 5x1
y
x2 s2
[0
3
0

12 +
x1  s1]
[0
1
1

8 
x1
]
[1
1
0

5x1
]
Replace R1 with (1/3)R1.
[0
1
0

4 +
(1/3)x1  (1/3)s1]
[0
1
1

8 
x1
]
[1
1
0

5x1
]
Replace R2 with R2  R1. Replace R3 with R3  R1.
[0
1
0

4 +
(1/3)x1  (1/3)s1]
[0
0
1

4 
(4/3)x1 + (1/3)s1]
[1
0
0

4 
(16/3)x1 + (1/3)s1]
y = 4  (16/3)x1 + (1/3)s1
x2 = 4 + (1/3)x1  (1/3)s1
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 Fall '09
 VLADIMIRLBOGINSKI

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