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?x1 12 23818283S4$1-201 10003823 0-2012061211-30010284-3 0200-1 1 42-20 1100-40-8b) Solve the following linear program using the 2-phase simplex algorithm. You should givethe initial tableau and each further tableau produced during the execution of thealgorithm. If the program has an optimal solution, give this solution and state itsobjective value. If it does not have an optimal solution, say why.maximize 21 - - 2x2 + x3 - 4x4subject to 2x1+x22x3x4≥ 1,5x1+x2-x3-4 -1,2x1+x2-x3-342,1, 2, 3, 4 ≥0.

Answered: Image /qna-images/answer/0db9d816-f205-4529-893e-36f6f85fefa5.jpg

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 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
Highlight rows and columns please
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
2. 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? X1 x2 X3 S1 S2 S3 S4 55 S1 -2 0 1 10 0 0 3 3 0 -20 1 2 0 6 ུཚ་ 1 1 -300 1 0 2 -30 2 0 0 -1 1 4 -20 11 00-40-8
Questions 1 and 2 handwritten in tableau form please, highlighting rows and columns
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.
Use the Simplex algorithm to solve the following LP.
Solve this linear programming problem by graphing. Give all answers correct to at least 2 decimal places. A company manufactures checker sets and chess sets. Suppose each day the company has available 1600 boards (which can be used for both games) and 80,000 units of wood for making pieces. Each checker set uses 20 units of wood and each chess set uses 60 units of wood. The distributors the company sells to can take up to 1250 checker sets per day and up to 750 chess sets per day. The company makes a profit of $1.00 on each checker set and $2.00 on each chess set. (a) How many checker sets and how many chess sets should the company make each day in order to maximize its profits? checker sets chess sets (b) What is the profit per day using this strategy? $ per day
+ 7. Consider the feasible region shown below. Assume the origin (A) is feasible and the constraints are all constraints and the variables are all nonnegative. Suppose you wish to maximize 1 + over this feasible region and you are currently at point G. Which variable should enter the basis in the first iteration of the simplex algorithm if we wish to maximize the objective function improvement after the first iteration? O only 2₂ only Ⓒ* only A 1.₂. or s 1 H B G A: (0,0,0) B: (1,0,0) C (0, 1, 0) D: (0, 0, 1)
please help with this true/false linear programming questions, thank you!

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