B. Convert primal problem to dual problem:Minimize Z = 4x₁ + 2x₂ = x3Subject to:x₁ + x₂ + 2x3 ≥ 32x₁2x₂ + 4x3 ≤ 5X1, X2, X3 20

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Answered: B. Convert primal problem to dual…

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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A rancher has 260 meters of fence with which to enclose three sides of a rectangular meadow (the fourth side is a cliff wall and will not require fencing). Find the dimensions of the meadow with the largest possible area. (For the purpose of this problem, the width will be the smaller dimension (needing two sides); the length with be the longer dimension (needing one side).) length = meters width= meters What is the largest area possible for this meadow? area = meters-squared Enter your answers as numbers. If necessary, round to the nearest hundredths.
Problem is in the image
(b) To find the number of shoes, a company should manufacture per day to optimally use their machine and assembly line. One needs to solve the following set of equations. The unknowns are the number for men, X1, women, x2, teenagers, x3, and infants, x4. 10x1 – x2 + 2x3 = 6 —х1 + 11х — хз+ 3x, 3D 25 2x1 – x2 + 10xX3 – X4 = -11 Зx2 — хз + 8хд 3D 15 Find approximate solutions to x1, x2, X3, and x4. Starting with x = (0, 0, 0, 0)" and iterating until ||x(*) – x*-)|. < 10-3 ||x(k) || .
2) REVIEW: On quiz 6 the profit function was y= x*(660-3x)-(8000+110x). We can multiply this out as y= 660x-3x-8000-110x. Use the POWER RULE to find x (the number of TVS to sell to get the most profit.) On quiz 6 we used the calculator's maximum program; we should get the same answer here using calculus.
Maximize z = 2x1 + 7x2 + x3 , subject to 2x1 + 7x2 + x3 ≤ 103 4x1 + x2 + 11x3 ≤ 239 with x1 ≥ 0, x2 ≥ 0 , x3 ≥ 0
If x² + 2y +3z? = x2 + 2y2 + 3z2 = x3 + 2y3 + 3z3 =2, and x₂x3 +2y2y3 +3z2z3 = x3x₁ +2y3v₁ +3Z3Z1 = x₁x₂ + 2y₁y₂ +3Z₁Z2 = 1, X1 then find the value of x2 X3 Y₁ Y₂ Y3 Z1 Z2 Z3
Derive and use 4 step-rule Show your solution in two questions: ( x+5 2 2 r¯ + 2 3 y= 3Vx+1 g(x) = and
6. Factor fully f (x) =12x* +17x-70x -33x+18
Q2. By using simplex method, maximise f = 2x, +3x, subjected to: 5x, +3x, <105 Зх, + 6х, < 126

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B. Convert primal problem to dual problem: Minimize Z = 4x₁ + 2x₂-x3 Subject to: x₁ + x₂ + 2x3 ≥ 3 2x₁2x₂ + 4x3 ≤ 5 X1, X2, X3 20