Q4: Consider the following LP Max z= 3x1 -3x2 Subject to: -X1 + 4x2 2 8 X1 + X2 5 6 X12 0, x2 unrestricted a) Solve the following LP optimally b) If a new variable x32 0 is added where c3=D0, a13=2, and a23=0, find the new optimal solution

Q4: Consider the following LP Max z= 3x1 -3x2 Subject to: -X1 + 4x2 2 8 X1 + X2 5 6 X12 0, x2 unrestricted a) Solve the following LP optimally b) If a new variable x32 0 is added where c3=D0, a13=2, and a23=0, find the new optimal solution

Name: Q4:Consider the following LPMax z= 3x1 -3x2Subject to:-X1 + 4x2 2 8X1
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: Q4:Consider the following LPMax z= 3x1 -3x2Subject to:-X1 + 4x2 2 8X1 + X2 s 6X12 0, x2 unrestricteda) Solve the following LP optimallyb) If a new variable x32 0 is added where C3=0, a13=2, and a23=0, find the new optimal solution

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 3BEXP

See similar textbooks

Related questions

Q: 9 Graphically determine two optimal solutions to the following LP: min z = 3x1 + 5x2 3x1 + 2x2 > 36…

Q: Graphically, solve the following problem using Branch and Bound Use x1 for branching. Problem Max…

A: Let us solve the given LPP by Branch and Bound method in the next steps.

Q: i. What is the optimal solution if es (coefficient of x) is increased to 6? ii. How much increase or…

Q: Consider the following linear program: maximize: 4r +2r2 +3r3 s.t. r1- 2r2 + 3r3 < 12 - r1 +3r2 +x3…

Q: Solve the following LP problems using graphical method. Clearly draw the feasible region,…

A: To solve the given linear programming problem graphically, we want to draw all the inequalities on…

Q: Solve the following LP using Simplex method Minimise Z = 60x1 + 80x2 Subject to 20x1 + 30x2 ≥ 900…

A: Given the problem is Minimise Z = 60x1 + 80x2 Subject to 20x1 + 30x2 ≥ 900 40x1 + 30x2…

Q: Q1:- How do you determine if an LP problem has alternative optimal solutions.…

A: An LPP is said to have alternative optimal solution or multiple solution if the non-basic variable…

Q: Consider the following all-integer linear program: Max 5x1 + 8x2 s.t. 5x1 + 5x2 < 32 9x1 + 3x2 < 38…

A: We are given an integer programming problem. Max 5x1 + 8x2s.t.5x1 + 5x2 ≤ 329x1 + 3x2 ≤ 38x1 + 2x2 ≤…

Q: Question 4- CHOOSE TRUE OR FALSE J/F-Every LP has an optimal solution. T/F-All parameters…

A: Since you have posted a question with multiple sub-parts, I will solve the first three subparts for…

Q: Solve the following LPP using the simplex / Big M Method Maximize: Z = 5X + 10Y Subject to the…

Q: Q2. Complete the following iteration tableau of Maximization problem of LPP and comment on the…

A: zj can be found using a formula or method as follows…

Q: Solve the following LP problems using graphical method. Clearly draw the feasible region,…

Q: 5. Solve the following maximization problem U (x, y) = x³ +24y max {x,y} s.t. x + 2y = 10 where x 20…

Q: Q2/Solve the following LPP using simplex method and answer the following question. Minimize P = 5x1+…

Q: Given is the following LP-problem. max Z = 7x1 + 5x2 + 6x3 + 8x4 + 2x5 4.x1 + 121 + 3x2 + 4.r3 + 5x4…

A: We solve the lpp by simplex method. And then find the dual problem of the given primal problem. To…

Q: max Z = x, +3x, s.t. 2. -x; +2x, 0

A: Graphical method

Q: Solve the following LP problems using graphical method. Clearly draw the feasible region,…

A: The problem is,max Z=x1+3x2such that -x1+2x2≤8x1≥0 and x2≥0

Q: Consider the following LP: 6x, + 4x2 4x, +x, s7 X, +x, 5 4 - X, + x, s 2 A. Maximize subject to…

Q: Q3. Complete the following iteration tableau of Maximization problem of LPP and comment on the…

A: Cj 2 1 0 0 0 Solution Cbi Basic Variable x1 x2 s1 s2 s3 2 x1 1 0 -1 0 0 30 1 x2 0 1 -2…

Q: . Solve by optimal control the problem: max 68. s.t. [ (ux − u² − x² )dt 1 x'=x+u, x(1)=2, x(5) =…

A: As per the question we are given a optimization problem where we have to find the optimal control…

Q: Consider the following LP. Max z= 5x, +2x, +3x, subject to X, +5x, +2x, = 30 X - 5x, - 6x, < 40 The…

A: The duality principle is the principle that optimization problems may be viewed from either of two…

Q: Consider the following constrained maximization problem:maximize y = x1 + 5 ln x2subject to k - x1 -…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Consider the following LP problem developed at Zafar Malik's Carbondale, Illinois, optical scanning…

A: Please see the attachment

Q: mar 3r1 + 212 s.t. F1 + 12 0) Suppose the z-line optimal simplex table of this problem is z + 7/3w,…

A: the given LPP is ; max Z =3x1+2x2s.t, x1+x2≤22x1-x2≤3x1,x2≥0 the problem is converted to canonical…

Q: Solve the given linear programming problem. Minimize z= 2x + 3y subject to x20, y2 0, x+ y2 3, 2x+…

A: Firstly make the graph of the inequalities and find all boundary point.

Q: 1. Consider the problem below: Min (z) = -2x-×2 Subject to: X1 + X25 5 2x1 + 3x2 S 12 X1 5 4 X1, X2…

Q: Find the optimal solution of the following problem. Min Ex+ 11Y s.t ex+ 3Y 2 27 7x+ 6Y 2 42 4x+ BY 2…

Q: Consider the problem: Min 10+ x² + y² subject to 2r² + y² ≥ 2, z≥0 and y≥ 0. T,Y 1. Suppose that…

A: Consider the problem, Minx,y10+x2+y2 subject to 2x2+y2≥2,x≥0 and y≥0. The objective is to write…

Q: Given the following conditions, determine the optimal solution. That is x1, x2 and a Te s0 3 -2(х, —…

A: As per the question we are gien all the partial derivatives of the lagrangian function of a…

Q: Consider the following LP. Мах z%3D2х, +10х, + бх, subject to X, +2x, + x, = 3 = 4 2x, — х, Xq,…

A: The duality principle is the principle that optimization problems may be viewed from either of two…

Q: Маx Z=5X1+2X2 S.T. 2X1+5X2 <10 4X1 - X2 < 12 X1+X2 < 4 X1,X2 2 0 Optimal solution is X1=3, X2=0 Z=…

A: We will solve the given LPP problem using the graphical method first we will find the region which…

Q: Find the optimal Solution of following transportation system formulated below by 1. Simplex method…

A: Let's solve by using simplex method.

Q: 1. Consider the following LP: Maximize z = x, + 3x, subject to *, + x, < 2 - x, + x, 5 4 x,…

Q: Given the LP problem, Maximize z = 5x + 2y subject to x + 3y < 5, 2x + y < 2, x + y < 3, х,у 20. a)…

Q: Solve the following LP problems using graphical method. Clearly draw the feasible region,…

Q: Consider the following LP. Max z = 4x, +8x, +8x, – 6x, subject to X, + X, + X3 = 4 X, + 4x, +x4 = 8…

A: We are given the following LPP : Max Z = 4x1 + 8x2 + 8x3 - 6x4 Subject to the constraints : x1 + x2…

Q: How many optimal basic feasible solutions does the following LP have? max z = 2x1 + 2x2 s.t. X1 + x2…

A: Draw the graph of the constraints

Q: Use the KKT conditions to solve the following problem: Min Z(X1 , X2) = 4(X1 -2)2 + 3(X2 – 4)3…

Q: Consider the following LPproblem 2x1+3r2 marimize z = %3D 3x2 0 (non negativity const a. The…

A: Let us solve this problem graphically Let us consider the 1st constraint as -x1+3x2=12 x1 0 -12…

Q: Consider the following linear program : z = 6x1 + 6x2 + 10x3 → min s.t. 4x1 + 3x2 + 2x3 ≥ 16 x1 +…

A: (a) First find primal to dual of LPP : Primal is (Solution steps of Primal by BigM method) MIN Zx…

Q: Determine which of the tableaus, if any: 6) A) Gives an infeasible solution. B) Gives an optimal…

A: In an LPP, there are many cases for example optimal solution, infeasible solution, unbounded…

Q: • Consider the following LP: maximize 2x1+ 5x2 s.t. -x1 + 2x2 < 5 2x1 + 3x2 < 12 X1 + x2 2 -1 X1, X2…

A: We are given the following LPP problem : maximize 2x1 + 5x2 s.t. -x1 + 2x2 ≤ 5 2x1 + 3x2 ≤ 12 x1 +…

Q: Q2. Complete the following iteration tableau of Maximization problem of LPP and comment on the…

A: Using Excel,

Q: Consider the LP model below: Маx z 3D х, + X2 șt. 4x1 + x2 < 100 X1 + x2 < 80 X1 S 40 X1, X2 2 0…

Q: Max 5x1 + 8x2 s.t. 5x1 + 6x2 ≤ 32 10x1 + 5x2 ≤ 46 x1 + 2x2 ≤ 10 x1, x2 ≥ 0 and…

Q: Consider the following LPP: Min Z 3 3X, + Х+ Xз Such that: X — 2X + Xз <11, -4X; + X, + 2X3 2 3…

A: Optimal primal table is given in the problem We know that optimal solution of both the primal and…

Topic Video

Question

Q4:
Consider the following LP
Max z= 3x1 -3x2
Subject to:
-X1 + 4x2 2 8
X1 + X2 s 6
X12 0, x2 unrestricted
a) Solve the following LP optimally
b) If a new variable x32 0 is added where C3=0, a13=2, and a23=0, find the new optimal solution

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step 8

Step 9

Step 10

Trending now

This is a popular solution!

Step by step

Solved in 10 steps with 9 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Optimization$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Find the optimal solution. MAX Z=6X+7Yst4X+5Y≤2010X+7Y≤353X+4Y≥6 X ≥0 ,Y ≥0 and an integer
Consider the following linear program: Max Z = -4x1 + 2x2 Subject To: -2x1 + 2x2 ≤ 7 x1 ≥ 2 x1 - 4x2 ≤ 0 2x1 + 2x2 ≥ 10 x1, x2 ≥ 0 Part A: Write the LP in standard equality form. Part B: Solve the original LP graphically (to scale). Clearly identify the feasible region and, if one or more exist, the optimal solution(s) (provide exact values for x1, x2, and Z).
Q3- Find the optimum values of X1, X2 and X3 that maximize the values of Z using simplex method? Maximize Z= 3X1+ 4X2+X3 Subject to 3X1 +10X2 +5X3 <120 5X1 +2X2 +8X3<6 4X1 +10X2 +3X3 < 105 X1,X2,X3 >0
2. Maximise 1170x1 + 1110x2Subject to: 9x1 + 5x2 ≥ 5007x1 + 9x2 ≥ 3005x1 + 3x2 ≤ 15007x1 + 9x2 ≤ 19002x1 + 4x2 ≤ 1000x1, x2 ≥ 0-Find graphically the feasible region and the optimal solution.
Consider the LP model and its corresponding graph below. Maximize z = 5x + 4ySubject to:3x + 2y <= 12x + 2y >= 8x >= 0y >= 0 From the given graph, what are the corner points of the feasible region? What are the values of x and y for the optimal solution? What is the maximum value of z?
Suppose following simplex table: 2 3 1 -1 0 0 -100 x1 x2 x3 x4 x5 x6 x7 b x5 0 7/2 0 0 3/2 1 1/2 -3/2 14 x3 1 5/2 0 1 1/2 0 1/2 1/2 13 x2 3 0 1 0 1 0 0 1 17 Z - C We can say, that: Select one: The solution is not optimal. The solution is optimal. The solution can be the initial solution.
5. Consider the following LP:Minimize z = 7x1 + 15x2 + 20x3, subject to the constraints2x1 + 4x2 + 6x3 ≥24,3x1 + 9x2 + 6x3 ≥30,x1, x2, x3 ≥0.a) Solve the given LP using big M method
Consider the following linear program : z = 6x1 + 6x2 + 10x3 → min s.t. 4x1 + 3x2 + 2x3 ≥ 16 x1 + 2x2 + 5x3 ≥ 16 x1, x2, x3 ≥ 0 a) 1. Build the dual problem corresponding to the given problem! b) Solve the dual problem graphically! Determine the exact coordinates by computing the intersection point of two appropriate lines! c) Conclude for the solution (objective and variables) of the primal problem by using the complementary slackness conditions.
Use two-phase simplex Method to solve the following LP Minimize z= 6 x1 + 3 x2 Subject to x1+x2 ≥ 1 2x1- x2 ≥ 1 3x2 ≤ 2 x1,x2 ≥ 0
Consider the following linear optimization model:Maximize z(x1, x2) = 4x1 + 4x2Subject to8x1 + 2x2 ≤ 165x1 + 2x2 ≤ 12x1, x2 ≥ 0(a) Draw the feasible region and label all the corners.(b) Obtain an optimal solution using graphical method
2. Use the standard simplex method to solve using your first pivot choice. Provide the sequence of points given in the tableau. Maximize: P=5x+4y Subject to: 2x+y<=80 2x+3y<=120 4x+y<=160 x>=0,y>=0