For the following problemMinimize W=2X1+10X2+8X3Subject toX1+X2+X3 26X2+2X3 2 8X1+2X2+2X324X1 20, X2 20 and X3 20Found the associated dual problemMaximize Z=6 Y1+8 Y2 +4 Y3Subject to1Y1+ 0Y2 + -1Y3 S2.1Y1+ 1Y2 + 2Y3 S101Y1+ 2Y2 + 2Y3 sY1 2 0,Y22 O and Y3 2 0Solve the dual problem and get the solution of the basic problem:X1=X2=and X3Dco

Name: For the following problemMinimize W=2X1+10X2+8X3Subject toX1+X2+X3 26
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: For the following problemMinimize W=2X1+10X2+8X3Subject toX1+X2+X3 26X2+2X3 2 8X1+2X2+2X324X1 20, X2 20 and X3 20Found the associated dual problemMaximize Z=6 Y1+8 Y2 +4 Y3Subject to1Y1+ 0Y2 + -1Y3 S2.1Y1+ 1Y2 + 2Y3 S101Y1+ 2Y2 + 2Y3 sY1 2 0,Y22 O a

To define the dual problem of the given primal problem, identify the number of variables and the…

Math

Advanced Math

For the following problem Minimize W=2X1+10X2+8X3 Subject to X1+X2+X3 26 X2+2X3 2 8 -X1+2X2+2X324 X12 0, X2 2 0 and X3 20 Found the associated dual problem Maximize Z= 6 Y1+ 8 Y2 + 4 Y3 Subject to Y1+ 0 Y2 + -1 Y3 S 1 Y1+ 1 Y2 + 2 Y3 S 10 Y1+ 2 Y2+ 2 Y3 S 08. Y1 2 0,Y22 0 and Y3 2 0 Solve the dual problem and get the solution of the basic problem: X1= ,X2= and X3=

For the following problem Minimize W=2X1+10X2+8X3 Subject to X1+X2+X3 26 X2+2X3 2 8 -X1+2X2+2X324 X12 0, X2 2 0 and X3 20 Found the associated dual problem Maximize Z= 6 Y1+ 8 Y2 + 4 Y3 Subject to Y1+ 0 Y2 + -1 Y3 S 1 Y1+ 1 Y2 + 2 Y3 S 10 Y1+ 2 Y2+ 2 Y3 S 08. Y1 2 0,Y22 0 and Y3 2 0 Solve the dual problem and get the solution of the basic problem: X1= ,X2= and X3=

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Consider the following optimization problem: Determine three positive real numbers such that their…

A: Solution

Q: a) Consider the following non-normal LP problem. Minimize z = x₁ - 3x₂ - 2x3 Subject to 3x₁-x₂ + 2x₂…

Q: max z = 3x₁ + Sx25x3 + 8x4 nx1 + x2 + x3 + 3x4 ≤ 7 -x₁- (s+n)x2 - X3 X4-2 X1, X2, X3, X4 20 -

A: (.) Given, (.) standard form of maximization problem is, then dual problem is given…

Q: .Consider the multiobjective LP given below max 6x1+4x2 max x2 st 3x1+2x2=0 with the targets of…

A: We draw the given constraints in order to get feasible region and corresponding extreme points or…

Q: [3.49] The following is the current simplex tableau of a given maximization problem. The objective…

Q: 1. Find the solution to the following LP problem using the big M method Minimization : Z = 6X₁ + 8X₂…

Q: . Consider the problem of maximizing xix, subject to the constraint 2x2 + x3 = 1. Find all critical…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: B. Convert primal problem to dual problem: Minimize Z = 4x₁ + 2x₂-x3 Subject to: x₁ + x₂ + 2x32 3…

Q: (2) Consider the following LPP maximize subject to a1x1 + Y +anxn+y-t = b x1, · · ·, xn, Y, t≥ 0,…

A: subject to We have to find the dual of the problem and solve it.

Q: [3.28] Consider the following problem: + 2x2 Maximize -3x₁ subject to 2x1 3x2 + 2x2 + -X1 -X1 X1, -…

Q: Maximize P = x1 + 2x2 + x3, Subject to: 3x1 + x2 + x3 <4 x1 + x2 + 2x3 < 4 æ1, X2, x3 and give the…

A: It is given that, Max P=x1+2x2+x3 Subject to the constraints, 3x1+x2+x3≤4x1+x2+2x3≤4and x1,x2,x3≥0…

Q: B. Convert primal problem to dual problem: Minimize Z = 4x₁ + 2x₂-x3 Subject to: x₁ + x₂ + 2x3 ≥ 3…

Q: 5.2-1. Consider the following problem. Maximize subject to x₂ + 2x₂ + 3x₂ + 3x₂ Z=8x₁ +4x₂+ 6 x3 +…

A: Adding slack variables x6,x7 and x8 in the first , second and third inequation respectively.Thus the…

Q: ¹) solve the following PDE Using method. Y 22x + x 22y = xy the multiplier

Q: b) Consider the following LP problem. Maximize z = 3x1 + 4x2 + X3 Subject to X1 + x2 + x, 5 50 2x, –…

Q: 3. Show that the LP problem Minimize: subject to g(x1, x2) = 2x1 - 5x2 x₁ + x₂ > 2 - x12x₂ ≤0 x22x11…

A: Given:- Minimize: gx1,x2=2x1-5x2Subject to :x1+x2≥2x2-2x1≤1x1,x2≥0

Q: 1. How much are three numbers worth if you want their product to be maximum and their sum to be…

A: Let us take the three numbers as u,v, and w so that uvw should be maximum and u+v+w = 1000

Q: 5. Consider the following problem Maximize Z = 2x₁2x₂ + 3x3, subject to -x₁ + x₂ + x3 ≤ 4 2x₁ - x₂ +…

Q: 2.SOLVE USING BIG-M METHOD Maximize 3x1 - x2 subject to X1 X2 ≤ 3 2x1 < x₂ x₁ + x₂ ≥ 12 X1, X₂ 20

Q: Consider the following problem: maximize P = ry subject to y = 3 – x and x>-1. What is the solution…

A: Here, we have to maximize the function P=xy, subject to the condition y=3-x2 and x≥-1. Now,…

Q: Consider the following 3D linear optimisation problem. maximize 2x2-x3+3 subject to r + a2+ a3 = 3…

A: The standard form of the given LPP is Maximize z=2x2-x3+3 subject to…

Q: Minimize g - 20x + 30y +36z subject to: x+2y +3z ≥ 48 2x + 2y +3z ≥ 70 2x +3y +4z ≥ 96

A: The given problem is: Minimize g - 20x + 30y +36z subject to: x+2y +3z ≥ 48 2x + 2y +3z ≥ 70 2x…

Q: 5. Use duality to show that the following LP has an optimal solution 2x1 - X2 Subject to 2x, -X2 - X…

Q: Consider Minimize 2x1+12 subject t. 3X1 + X2 39 x7 +2x2 38 X1 + 6X₂ 7/12 X1, X2710 y solve this…

Q: [3.47] The following is the current simplex tableau of a linear programming problem. The objective…

Q: 3) f(x1, x2) = -2x + 3x² - 8x1x2 + 3x1 + 3x2 Restrictions 3x² + x2 = 10 4x + 2x² = 12 Solve the…

A: ## Resolving the Equation System: Now let us solve the system of equations for x1, x2, λ₁, and λ₂…

Q: 4.1-2. Consider the following problem. Z = 3x₁ + 2x₂, Maximize subject to 2x₁ + x₂ ≤ 6 x₁ + 2x₂ ≤ 6

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: 22x1 + 44x2 + 33x3 subject to x1 + 2x2 + x3 > 3, x1 + x3 > 3, 3x1 + 2x2 + 2x3 > 8 using two…

A: i) Dual problem: Primal is MIN Zx = 22 x1 + 44 x2 + 33 x3 subject to x1 +…

Q: Suppose that a company needs 5 ×10,000 items during a year and that preparation costs are $5 for…

Q: subject to I1 x₂ = 2 = Use the simplex method to maximize 2= 7x₁ + 13x₂ 521 x 1 x1 X2 + + > X2 < 10…

Q: Let’s solve Example 2 from Section 3.1. We found that the linear programming problem was:Minimize C…

A: We have to graph the given conditions first.60x+40y ≥ 24096x+160y ≥ 672We make tables for auxiliary…

Q: 1. Minimize z = 3x, + 4x2 subject to x, + 4x2 > 8 2x1 + 3x2 2 12 2х, + х, 2 6 х, 20, х, 2 0. 2.…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Use the graphical method to find the optimal solutions of the following LP Problem. Max. Z = 3x1 +…

A: Max Z=3x1+5x2s.t3x1+2x2≤18x1≤4x2≤6x1, x2≥0

Q: _2. Solve the problem minimize f(x) = -xỉ +x3 – x,x2 subject to 2x1 – x2 > 2 X1 + x2 0. |

Q: 4 Show that if ties are broken in favor of lower-numbered rows, then cycling occurs when the simplex…

A: Given: max z=-3x1+x2-6x39x1+x2-9x3-2x4≤0x1+x23-2x3-x43≤0-9x1-x2+9x3+2x4≤1xi≥0 (i=1, 2, 3, 4) To…

Q: D,I 3.1-6. Use the graphical method to solve the problem Maximize Z = 10x₁ + 20x2, subject to -x₁ +…

A: In this question, we will solve the LPP by using graphical method.

Q: Consider the famous Hydit-Filit problem, but with c₂ the coefficient of x2 in the objective…

A: Given Problem: Maximize Zx=140x1+c2x2 such that, 2x1+4x2≤28 5x1+5x2≤50 x1≤8, x2≤6 x1≥0, x2≥0 To…

Q: 6.6. Consider the following linear programming problem. maximize z = 3x + 10x₂ + 5x3 + 11x4 + 6x5 +…

Topic Video

Question

100%

For the following problem
Minimize W=2X1+10X2+8X3
Subject to
X1+X2+X3 26
X2+2X3 2 8
X1+2X2+2X324
X1 20, X2 20 and X3 20
Found the associated dual problem
Maximize Z=
6 Y1+
8 Y2 +
4 Y3
Subject to
1
Y1+ 0
Y2 + -1
Y3 S
2.
1
Y1+ 1
Y2 + 2
Y3 S
10
1
Y1+ 2
Y2 + 2
Y3 s
Y1 2 0,Y22 O and Y3 2 0
Solve the dual problem and get the solution of the basic problem:
X1=
X2=
and X3D
co

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step by step

Solved in 6 steps

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

3. Consider the following dual problem Minimize Z = 7x₁ + 2x₂ + 5x3 + 4x4 subject to 2x₁ + 4x₂ + 7x3 + x4 ≥ 5 8x₁ + 4x2 + 6x3 + 4x4 ≥ 8 3x₁ + 8x₂ + x3 + 4x4 ≥ 4 and x₁ ≥ 0, x₂ ≥ 0, X3 ≥ 0, X4 ≥ 0. (a) Construct the primal problem corresponding to this problem. (b) Solve the primal problem by the original simplex method (in tabular form) step by step. Identify the complementary basic solution for the dual problem obtained at each iteration. Use the dual simplex method manually to solve the dual problem. Compare the resulting sequence of basic solutions with the complementary basic solutions obtained in part (b). (c)
Q1. Given the following multi-objective problem (A): max 2X, + 0.5X2 + Xҙ (Z1) (Z2) (Z3) min 4X1 – 3X2 + X3 min X2 – 2X3 s.t. (1) 4X1 + X3 < 10 5X1 + X2 < 20 X; are non-negative Formulate this problem using Global Criterion (GC) method and Compromise Programming (GP) method.
5. The nonlinear system xỉ – 10x1 + x, = -8, x1x3+ x1 – 10x2 + 8 = 0 can be transformed into the fixed-point problem xž + x3 + 8 x1x3 + x1 + 8 X1 = 91(x1, x2) x2 = 92(x1, x2) 10 10 (a) Show that G (91, 92)* mapping D into R? has a unique fixed point in D = {X = (x1, 82)' : 0 < x; < 1.5, i = 1, 2}. (b) Apply functional iteration to approximate the solution.
Q4. Solve the following problem using the simplex method: Minimize z = x- 4y Subject to 2x - 3y <6 x +y<3 x2 0, y 20
2 Minimize subject tos X+2x2 +3x3-12 0 X2+ 2x3+3x4- 4 0 by direct substitation method.
[3.27] Consider the following problem: Maximize 2x₁ subject to X1 2x1 X1 X1, + x2 + 2x₂ + 3x2 x2, + 6x3 + 4x3 + x3 X3 X3, 11+ + 4x4 ********* X4 X4 ≤6 < 12 2 ≤ X4 X4 2 0.
subject to x1 = x₂ = Z Use the simplex method to maximize z = 6x₁ + 11x2 3x₁ x 1 x1 X2 + X2 0 > 0
New program: Objective function: Maximize Z = 2x, + xz + 3x3 + Os, + Os, + Os3 Subject to: X + x2 + 2x, + 1s, = 25 (1) X + X, + 1s2 = 8 (2) X2 + X3 + 1s, = 10 (3) X1, X2, X3, 15,, 1s2,1s, 20
P.nil
4. Consider the following optimization problem Min f(x) = x,-2*2+523-ни s.t. 2x₁-3x₂=-5 -x3+2x473 -22₂ + 3x3 + x47-6 43 3x₁-4₂+7x4-1 トレ x₁^3 Z. (a) Convert the problem to conventional form. (b) Convert the problem to standard form.
Question 29 Maximize 2x1 + 4x2 subject to x1 + 3x₂ �� 12 2x1 + x₂ ≤ 14 120 and ₂ > 0 Using simplex method by introducing slack variables 3 and 4, and M = 2x1 + 4x2, now the inequalities are changed to equations x1 + 3x2 + x3 = 12 (1) 2x1 + x₂ + x4 = 14 (2) 2x14x2 M = 0 (3) To bring 1 and 2 into the solution, which one (1 or 2) is firstly brought into the solution and which equation is used as the pivot equation. O1 and (2) O #2 and (3) O2 and (2) O #1 and (1) O2 and (1)
Sand is being dumped from a hopper railcar at a rate of 40 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal to each other (both are growing larger as more sand is dumped). How fast is the base diameter increasing when the base is 18 feet long? Round your answer to three decimal places. ft/min