a) Suppose that we are carrying out the 1-phase simplex algorithm on a linear program instandard inequality form (with 3 variables and 4 constraints) and suppose that we havereached a point where we have obtained the following tableau. Apply one more pivotoperation, indicating the highlighted row and column and the row operations you carryout. What can you conclude from your updated tableau?x1x2 x381 82838481-2 01 1 0003823 0-2 012061211-30010284-3 0200 -114-2 -2 01100-40-8

Step 1: To proceed further in the given simplex table: First, check the most negative entry from…

Answered: a) Suppose that we are carrying out the…

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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Suppose that we are carrying out the 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? I1 I2 23 S1 S2 $3 SA $1 -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 SA -3 0 2 0 0 -1 1 4 -2 -2 0 11 0 0 -4 0-8
Solve the following linear programs (LPs) using the simplex algorithm. • For each tableau you obtain, write the associated BFS and its objective value. • For each LP, find the complete optimal solution set and write it using appropriate mathematical notation. Use only the information in the tableaux to justify your answer. minimize z(x1, x2) subject to -x1 X2 + x2 0
An advertising firm has D dollars to spend on reachingcustomers in T separate markets. Market t consists of ktpeople. If x dollars are spent on advertising in market t, theprobability that a given person in market t will be reachedis pt(x). Each person in market t who is reached will buy ctunits of the product. A person who is not reached will notbuy any of the product. Formulate a dynamic programmingrecursion that could be used to maximize the expectednumber of units sold in T markets.
Solve each of the following linear programs using the 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. Ideally you should indicate the highlighted row and columns in each pivot step as well as the row operations you carry out. 2. maximize 2x₁ + 4x₂ subject to - 13 -2x1 + x3 ≤ 3, 1x12x2 + 4x3 ≤ 2, x1 + x2-3x3 ≤ 2, 2x₁x₂ + x32-6, T1, T2, T3 20
Explain the purpose of artificial variables and slack variables in the context of the 2-phase simplex algorithm. Specifically, for both kinds of variables explain why are they introduced, what each one of them measures, and what we can conclude when they are set to zero. 6.
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
Please explain
Glenmont Corporation wants to select 1 project from a set of 4 possible projects. Which of these constraints ensures only 1 project is selected? X1 + X2 + X3 + X4 ≥ 0 X1 + X2 + X3 + X4 ≥ 1 X1 + X2 + X3 + X4 = 1 X1 + X2 + X3 + X4 ≤ 1
please help with this true/false linear programming questions, thank you!
Apply the first phase of the 2-phase simplex algorithm to the following linear pro- gramme giving the initial tableau and each further tableau produced. Give the starting tableau for the second phase if there is one. maximize 2x1 + x2+3x3 subject to x2-x32, 1+3x2+2x3 ≥ 3, 2x1 +22+3 = 4, x1, x2, x3 0.
Which of the following in a simplex table indicates that an optimal solution for a minimization problem has been found? Oa All the (C)- Zi) values are positive or zero Ob All the Z values are negative or zero OC All the Zj values are positive or zero All the (C/- Z) values are positive od All the ( Cj- Z) values are negative or zero
Solve the following linear programs (LPs) using the simplex algorithm. • For each tableau you obtain, write the associated BFS and its objective value. • For each LP, find the complete optimal solution set and write it using appropriate mathematical notation. Use only the information in the tableaux to justify your answer. maximize z(x1, x2, x3) = subject to -2x1 + 4.x3 + 2.x3 0

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