Given the following 2 constraints, which solution is a feasible solution for a maximization problem?(1) 7 x1 + 3 x2 s 21(2) x1 - x2 s 3O (x1, x2) - (2, 1)O x1. x2) - (5, 1)O (x1, x2) - (4, 4)O (x1, x2) - (1, 5)

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Answered: Given the following 2 constraints,…

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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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.
[3.6] Consider the following problem: Maximize - 3x₁ subject to -X1 + a. b. 2x2 2.x1 + 3x2 X1 x2 X₂ VIVINA ♡ N -com 1 6 0 24/3. S Solve the problem graphically. Set up the problem in tableau form for the simplex method, and obtain an initial basic feasible solution.
(FAB 4) Use Lagrange Multipliers to find the maximum and minimum values of f (x, y) = 81x² + yšubject to the constraint 4x2 + y? = 9
QUESTION 14 Calculate the maximum value of 4x + 6y subject to the constraints below: 3x + y ≤ 16 x + 3y ≤ 16 y≥ 1 x ≥ 0
2 2. (10 pts) Consider the product XY where x and y are positive numbers which 2, must sum to six (6). Find the maximum value of xy under this contraint. a. Write the constraint equation. b. Use the equation in (a) to write the objective function in terms of the variable x. C. Apply the necessary calculus to solve the problem. Be sure to include a verification step, i.e. why your solution is the maximum. Also, give the maximum value.
& Determine the feasible space for each of the following independent constraints, given that t₁, ₂20. *(a) -3x₁ + x₂ ≤ 6. (b) x2x₂ 2 5. (c) 2x - 3r₂ = 12. (d) x₁x₂ = 0. *(e) -x₁ + x₂ 2 0.
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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)
Мах Z 3D 4x, + 3xz st. 2x1 < 12 (1) 2 x2 < 24 (2) Зх, + 2х, < к (3) X1 (4) x2 2 0 (5) Given the following the LP. Write a relevant integer value for K such that the problem remains feasible and the constraint (3) becomes redundant. A relevant value for K =
Consider the following optimization problem: max x1 + 2x2 -x1 + x2 >= -4 x1 + x2 <= 15 - x1 + 3x2 <= 25 x2 >= 0 Graph the polyhedron corresponding to the set of feasible solutions of (P). Is the set of feasible solutions a polytope (bounded polyhedron)?

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Given the following 2 constraints, which solution is a feasible solution for a maximization problem? (1) 7 x1 + 3 x2 s 21 (2) x1 - x2 s 3 O (x1, x2) - (2, 1) O x1. x2) - (5, 1) O x1, x2) - (4, 4) O (x1, x2) - (1, 5)