EBK MATHEMATICS FOR MACHINE TECHNOLOGY
7th Edition
ISBN: 9780100548169
Author: SMITH
Publisher: YUZU
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Chapter 82, Problem 37A
To determine
The decimal number
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a) Suppose that we are carrying out the 1-phase simplex algorithm on a linear program in
standard inequality form (with 3 variables and 4 constraints) and suppose that we have
reached a point where we have obtained the following tableau. Apply one more pivot
operation, indicating the highlighted row and column and the row operations you carry
out. What can you conclude from your updated tableau?
x1
x2 x3
81 82
83
84
81
-2 0
1 1 0
0
0
3
82
3 0
-2 0
1
2
0
6
12
1
1
-3
0
0
1
0
2
84
-3 0
2
0
0 -1
1
4
-2 -2 0
11
0
0-4
0
-8
b) Solve the following linear program using the 2-phase simplex algorithm. You should give
the initial tableau, and each further tableau produced during the execution of the
algorithm. If the program has an optimal solution, give this solution and state its
objective value. If it does not have an optimal solution, say why.
maximize ₁ - 2x2+x34x4
subject to 2x1+x22x3x41,
5x1 + x2-x3-×4 ≤ −1,
2x1+x2-x3-34
2,
1, 2, 3, 40.
Chapter 82 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
Ch. 82 - Prob. 1ACh. 82 - Prob. 2ACh. 82 - Prob. 3ACh. 82 - Prob. 4ACh. 82 - Prob. 5ACh. 82 - Prob. 6ACh. 82 - Prob. 7ACh. 82 - Prob. 8ACh. 82 - Prob. 9ACh. 82 - Analyze the following numbers. 0.802
Ch. 82 - Prob. 11ACh. 82 - Prob. 12ACh. 82 - Prob. 13ACh. 82 - Prob. 14ACh. 82 - Prob. 15ACh. 82 - Prob. 16ACh. 82 - Prob. 17ACh. 82 - Prob. 18ACh. 82 - Prob. 19ACh. 82 - Prob. 20ACh. 82 - Prob. 21ACh. 82 - Prob. 22ACh. 82 - Prob. 23ACh. 82 - Prob. 24ACh. 82 - Prob. 25ACh. 82 - Prob. 26ACh. 82 - Prob. 27ACh. 82 - Prob. 28ACh. 82 - Prob. 29ACh. 82 - Prob. 30ACh. 82 - Prob. 31ACh. 82 - Prob. 32ACh. 82 - Prob. 33ACh. 82 - Prob. 34ACh. 82 - Prob. 35ACh. 82 - Express the following binary numbers as decimal...Ch. 82 - Prob. 37ACh. 82 - Prob. 38ACh. 82 - Prob. 39ACh. 82 - Prob. 40ACh. 82 - Prob. 41ACh. 82 - Prob. 42ACh. 82 - Prob. 43ACh. 82 - Prob. 44ACh. 82 - Prob. 45ACh. 82 - Prob. 46ACh. 82 - Prob. 47ACh. 82 - Prob. 48ACh. 82 - Prob. 49ACh. 82 - Prob. 50ACh. 82 - Prob. 51ACh. 82 - Prob. 52ACh. 82 - Express the following decimal numbers as binary...Ch. 82 - Prob. 54ACh. 82 - Prob. 55ACh. 82 - Prob. 56ACh. 82 - Express the following decimal numbers as binary...
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- Suppose we have a linear program in standard equation form maximize cTx subject to Ax = b. x ≥ 0. and suppose u, v, and w are all optimal solutions to this linear program. (a) Prove that zu+v+w is an optimal solution. (b) If you try to adapt your proof from part (a) to prove that that u+v+w is an optimal solution, say exactly which part(s) of the proof go wrong. (c) If you try to adapt your proof from part (a) to prove that u+v-w is an optimal solution, say exactly which part(s) of the proof go wrong.arrow_forwarda) Suppose that we are carrying out the 1-phase simplex algorithm on a linear program in standard inequality form (with 3 variables and 4 constraints) and suppose that we have reached a point where we have obtained the following tableau. Apply one more pivot operation, indicating the highlighted row and column and the row operations you carry out. What can you conclude from your updated tableau? x1 x2 x3 81 82 83 84 81 -2 0 1 1 0 0 0 3 82 3 0 -2 0 1 2 0 6 12 1 1 -3 0 0 1 0 2 84 -3 0 2 0 0 -1 1 4 -2 -2 0 11 0 0-4 0 -8arrow_forwardPlease solve number 2.arrow_forward
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