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Subject
Excel
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Homework
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When you perform the primal simplex method, you are supposed to use Dantzig’s rule to
choose entering columns. Instead of floating point arithmetic, it is recommended to do
arithmetic with fractions. Solve the problems using the methods you learned in class (Optional
ways you google will not earn any point).
1. Dual Simplex Method
1-1. (5 points) Solve the following LP by Dual-Simplex:
min 5 x
1
+ 2 x
2
+ 3 x
3
+ 8 x
4
= z,
st 3 x
1
+ 2 x
2
6,
2 x
1
+ 4 x
2
+ x
3
+ 5 x
4
8,
x
1
, x
2
, x
3
, x
4
are all non-negative.
B Cb P x1 x2 x3 x4 x5 x6 x7 x8 x9
5 2 3 8 0 0 M M M
x1 5 1 1 0 -0.25 -1.25 -0.5 -0.25 0.5 0 0
x2 2 1.5 0 1 0.38 1.88 0.25 0.38 -0.25 0 0
x8 M 0 0 0 0 0 0 0 0 1 0
x9 M 0 0 0 0 0 0 0 0 0 1
min 8 0 0 -3.5 -10.5 -2 -0.5 -M+2 0 0
z=8
x1=1
x2=1,5
x3=0
x4= 0

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1-1-1. Coefficient Matrix
x
1
x
2
x
3
x
4
s
1
s
2
min
5
2
3
8
0
0
z
2
0
0
– 1
0
6
4
1
5
0
– 1
8
Ratio

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When you perform the primal simplex method, you are supposed to use Dantzig’s rule to choose entering columns. Instead of floating point arithmetic, it is recommended to do arithmetic with fractions. Solve the problems using the methods you learned in class (Optional ways you google will not earn any point). 1. Dual Simplex Method 1-1. (5 points) Solve the following LP by Dual-Simplex: min 5 x1 + 2 x2 + 3 x3 + 8 x4 = z, st 3 x1 + 2 x 2 ≥ 6, 2 x1 + 4 x2 + x3 + 5 x4 ≥ 8, x1, x2, x3, x4 are all non-negative. B Cb P x1 x2 x3 x4 x5 x6 x7 x8 x9 5 2 3 8 0 0 M M M x1 5 1 1 0 -0.25 -1.25 -0.5 -0.25 0.5 0 0 x2 2 1.5 0 1 0.38 1.88 0.25 0.38 -0.25 0 0 x8 M 0 0 0 0 0 0 0 0 1 0 x9 M 0 0 0 0 0 0 0 0 0 1 8 0 0 -3.5 -10.5 -2 -0.5 -M+2 0 0 min z=8 x1=1 x2=1,5 x3=0 x4= 0 1 1-1-1. Coefficient Matrix x1 x2 x3 x4 s1 s2 min 5 2 3 8 0 0 z 3 2 0 0 –1 0 6 2 4 1 5 0 –1 8 Ratio 2 1-1-2. Find the simplex tableau with respect to the initial basis B0 = {s1, s2}. Is it feasible? (Circle Yes/No) If no, perform the dual simplex method. Circle the leaving basic variable will leave out of the basis. Perform the minimum ratio test to determine the entering column. Circle the entering pivot. B Cb P x1 x2↓ x3 x4 x5 x6 x7 x8 6 8 0 0 0 0 0 0 Q x5 0 5 3 2 0 0 1 0 0 0 2.5 x6 0 2 2 4 0 0 0 1 0 0 0.5 x7 0 3 0 1 0 0 0 0 1 0 3 x8 0 8 ...
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Anonymous
Awesome! Perfect study aid.

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