Answered: An incomplete intermediate simplex… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.3: Systems Of Inequalities

Problem 13E

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Question

An incomplete intermediate simplex table for an LPP is given below:
1
3
-2
0
0
Cj
CB
Basis
X₂
X5
Z₁ - Cj
The basic variables are:
Select one:
12,3 and IĄ
O 11,3 and
12,4 and Is
12 and 13
XB
10
3
1
5/2
-1/2
-5/2
-1/2
X₂
6105
0
أنت
2
780
2
X4
1
OO
0
0
0
1/4
14
-34
3/4
0
X6
0
0
1
0

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show step on how to get the simplex method of this with the simplex method table
construct the initial plus one simplex tableaux for the following LPP: Max Z = X1 + 2x2 + 4x3 st : X1+X2 + X3 ≤ 400 x2+2x3 ≤ 300 x1 + x2 ≤ 200 x1, x2, x3 ≥ 0
Consider the following LP:Maximize z = 16x1 + 15x2subject to40x1 + 31x2 <=124-x1 + x2<= 1x1<=3x1, x2 >= 0(a) Solve the problem by the simplex method, where the entering variable is thenonbasic variable with the most negative z-row coefficient.
Question4: The simplex table obtained from an enterprise that produces three products under three constraints: machine hours, raw materials and meeting demand is given.Write down the primary and binary results and how the conclusion was reached.X₁ = ?X₂ = ?X₃ = ?S₁ = ?S₂ = ?S₃ = ?L₁ = ?L₂ = ?
Use the simplex algorithm to solve the following linear optimisation problem: maximisef(x1,x2,x3)=3x1+x2+2x3 subjectto: 3x1 +2x2 +x3 ≤8 x1 +2x2 +2x3 ≤4, x1,x2,x3 ≥0. You must address each of the 5 steps of the algorithm as presented in the course notes and videos in your answer.
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Analyze algebraically what special case in simplex application is present in each of the LP model below. Give an explanation to support your answer. a) Maximize z = 4x1 + 2x2 Subject to: 2x1 - x2 ≤ 2 3x1 - 4x2 ≤ 8 x1, x2 ≥ 0b) Maximize z = 3x1 + 2x2 Subject to: 4x1 - x2 ≤ 8 4x1 + 3x2 ≤ 12 4x1 + x2 ≤ 8 x1, x2 ≥ 0
Consider the following LP:min 5x1 + 4x2s.t. x1 + x2 ≥ 12x1 − x2 ≥ 13x2 ≤ 2x1, x2 ≥ 0.1. Write down the dual of this LP.2. We know that by strong duality, we can either solve this LP or its dual form to get the sameoptimal objective value. If you apply the simplex algorithm, which one would you rathersolve? Make your choice and apply the simplex algorithm to solve it.
First 3 parts are solved. 5-28 Consider the linear programmax x1 + x2s.t. x1 + x2 ≤ 9-2x1 + x2 ≤ 0x1 - 2x2 ≤ 0x1, x2 ≥ 0(a) Solve the problem graphically.(b) Add slacks x3,c, x5 to place the modelin standard form.(c) Apply rudimentary simplex Algorithm 5Ato compute an optimal solution to yourstandard form starting with all slacks basic.(d) Plot your progress in part (c) on thegraph of part (a).(e) How can the algorithm be making progress when l = 0 if some moves of part(c) left the solution unchanged? Explain.5-29 Do Exercise 5-28 for the LPmax x1s.t. 6x1 + 3x2 ≤ 1812x1 - 3x2 ≤ 0x1, x2 ≥ 0
Solve the following LP model using the simplex method.
4.1. #6 Complete the initial simplex table.

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