Problem 1) .shown below. Use the information in the tableau to answer the following questions:Simplex method is used to solve a LP problem. The final tableau is1.1. Which constraints are binding?1.2. What is the optimal solution of the dual model?BasisX1X2S1S2S3S4Rhs10241480X11-0.5-0.46S4-0.50.212S30.5-0.412X210.5-0.24

1.1 Binding constraints are those where optimal solution is on the line of the constraint.

Answered: Problem 1) . ; Simplex method is used…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Solve the following using Simplex Method. 1. A factory makes three types of chairs, A, B, and C. The factory makes a profit ci P200 on chair A, P300 on chair B, and P400 on chair C. Chair A requires 30 man-hours, chair B requires 20, and chair C requires 10. Chair A needs 2m2 of wood, chair needs 5m2, and chair C needs 3m2. Given 100 man-hours and 15m2 of wood per week, how many chairs of each type should be made each week to maximize profit? 2. Maximize Z = 8x +6 x Subject to: 10x,+ X2s 12 2xi+ 5 x2s 16 X120 INH
3. Find the dual of the LP problem given below. Z max = 4x + 2x2 +5x3 Constraints: X + x, 2 2 Зx, + х2 — х; <12 5x, + 2х, + 3х; <15 Sign Restriction: х, 20 х, 20, х, 20
A Section 7.2 - Math 176, section D X Bb Student Resources - Blackboard x M Mathway | Precalculus Problem x s What are the dimensions of a rec + i webassign.net/web/Student/Assignment-Responses/submit?dep=25867576&tags=autosave#Q4 Solve the system by the method of elimination. (If there is no solution, enter NO SOLUTION. If the system is dependent, enter a for x and enter y in terms of a.) 2x - 3y = 7 -4x + 6y = -14 7 (х, у) - (| х, — 2x 3 3 y 4 2 -2 6 Need Help? Read It 4 V i 7:24
2. a) Mathematical model and 1. simplex table of a LP problem is given below. Specify the special case in this problem and explain its reason. Z max = 3x, + 2x2 Cj 3 -M Constraints: S1 A1 RHS X1 X2 V1 X¡ +2x, <6 Xj 2 7 저20, x2 20 X1 3 1 2 1 Aj -M -2 -1 -1 1 1 Zj 3 6+2M 3+M M -M 18-M C;-Zj 0 -4-2M -3-M -M b) Mathematical model and 2. simplex table of a LP problem is given below. Specify the special case in this problem and explain its reason. Cj 1 -M Z max = x +2x2 Constraints: X1 X2 V1 A1 RHS X2 2 1 1 4 X1 +x, 21 Vị -1 1 -1 1 3 x2 <4 2 2 8. Zj 1 저20, x, 20 Cj-Zj -M -2
2. Analyze algebraically what special case in simplex application is present in each of the LP model below. Give an explanation to support your answer. b) Maximize z = 3x₁ + 2x2 Subject to: 4x11x28 4x1 + 3x2 ≤ 12 4x1 + 1x2 ≤8 X1, X2 ≥ 0
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Problem I. Least Square (10 points) a) Consider Y = AX+ V and VM (v|0, Q), what is the least square solution of X? b) If there is a constraint of b¹X= c, what is the optimal solution of X? c) If there is an additional constraint of XX=d, in addition to the constraint in b), what is the optimal solution of X?
min x1 + x2 s.t. 3x1 + 2x2 ≥ 36 3x1 + 4x2 ≥ 48 x1, x2 ≥ 0 For the LP problem above, which are the binding constraints? 3x1 + 2x2 ≥ 36 3x1 + 4x2 ≥ 48 x1 ≥ 0 x2 ≥ 0
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)
Choose the correct answer .
The following intermediate tableau for a dual maximum problem was obtained using the simplex method for optimizing a minimum problem. (see image) Perform all the necessary pivot and row operations to obtain the final tableau. Then, using the final tableau, answer the following questions: The minimum function value is: The value of x1 in the minimum problem is : The value of x2 in the minimum problem is:
2. 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 3x14x2 ≤ 8 X1, X2 ≥ 0

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