Solve this LP problem:1. Maximize z = 20x₁ + 10x₂ + x3Subject to: 3x₁ - 3x₂ + 5x3 ≤ 50x₁ + x₂ ≤ 10x₁-x₂ + 4x₂ ≤ 20X₁, X₂, X₂ ≥ 0Requirements:a)By inspecting the constraints, determine the direction (x₁, x₂, or x²) in whichthe solution space is unbounded. Support your answer.b) Verify using simplex calculation.

(a) To determine the direction in which the solution space is unbounded, we can inspect the…

Answered: Solve this LP problem: 1. Maximize z =…

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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Consider the following minimum problem: Minimize: C = 2x₁ + 3x₂ Subject to the constraints: x1 + x₂ > 2 2x1 + 3x₂ ≥ 6 x1 ≥ 0 x₂ > 0 Write the dual problem for the above minimum problem by selecting the appropriate number for each blank box shown below (Do not solve the dual problem). Y₁+ [Select] P [Select] = [Select] [Select] Y₁ ≥ 0 Minimum value of C = Value of 1 = Y2 ≥ 0 Value of 2 = Subject to the constraints: 3x1 + x₂ ≥ 6 -4x1 + 2x₂ ≥ 2 x₁ ≥0 X₂ ≥0 Use the simplex method to solve the following minimum problem on your own paper. Then, using your final tableau, enter the answer in each relevant box provided below. Minimize: C = 3x₁ +4x2 Subject to the following constraints: 2x1 + x₂ > 2 2x1 + x₂ ≥ 6 x₁ ≥ 0 ; x₂ > 0 x1 = Y₁+ X2 = Yı+ C = [Select] [Select] Use the simplex method and the Duality Principle to solve the following minimum problem: Minimize: C = 2x1 + 2x₂ Y2 Y22 y2 ≤ 3 and using your final tableau answer the questions below by entering the correct answer in each blank box.…
A cylindrical tank with a closed top is to be constructed to hold a fixed volume of 16, 0007 m³. Find he dimensions of the tank (radius r and height h) with the smallest possible total surface area. ou must justify your answer really does give the minimum surface area. constraint equation in terms of r and h: objective function in terms of r: dimensions of optimal tank (in meters): radius (r) Allqmie height (h)
This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, у) 3D 4x + 8y; х? + у2 = 20 maximum value minimum value
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Vipul
a) Write the dual to the following LPPS: i) Maximize: z= 3x, + 5x. + 4x. ii) Minimize: z= 3x. + 5x. + 2x. subject to: 2x. + X. + 4x 2 subject to: 2x. + 3х 23 3х - 3х+ 2х —8 with: x, x 20 with: x, <0

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