Use the simplex method to solve the problem.MinimizeP=2x, -5x2subject to5x, +3x, > 15The minimum value of Z is at x, = and x, =.(Simplify your answers.)

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Description: Use the simplex method to solve the problem.MinimizeP=2x, -5x2subject to5x, +3x, > 15The minimum value of Z is at x, = and x, =.(Simplify your answers.)

Given function to optimize Minimize P=2x1-5x2 Subject to x1+x2≤45x1+3x2≥15x1,x2≥0 To solve this…

Answered: Use the simplex method to solve the…

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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Use the simplex method to solve the problem.
Minimize
P=2x, -5x2
subject to
5x, +3x, > 15
The minimum value of Z is at x, = and x, =.
(Simplify your answers.)

Expert Solution

Step 1

Given function to optimize

Minimize $P = 2 x_{1} - 5 x_{2}$

Subject to

$x_{1} + x_{2} \leq 4 5 x_{1} + 3 x_{2} \geq 15 x_{1}, x_{2} \geq 0$

To solve this first introduce slack variable , surplus variable and artificial variable.

Minimize $P = 2 x_{1} - 5 x_{2} + 0 s_{1} + 0 s_{2} + M A_{1}$

Subject to

$x_{1} + x_{2} + s_{1} = 4 5 x_{1} + 3 x_{2} - s_{2} + A_{1} = 15 x_{1}, x_{2}, s_{1}, s_{2}, A_{1} \geq 0$

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