Help me fast so that I will give Upvote.... QUESTION 6find the maximum value of the objective function P=4x 2y subject tox+2ys 123x + ys 21X20y20the initial simplex tableaur if needed, plese input fractions like 1/2,-1/2, 1/12, 13/5constantrowrow2row3.pivot column is(here input xor y pivot row is row(here input 1,2 or 3)the simplex tableau ( the last tableauM.constantrow1.rowrowthe maximum value of objective function is

Answered: find the maximum value of the objective…

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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Expert Solution

Step 1

Note:- In given problem you don't mention about M, is it coefficient of artificial variable or it denotes Minimum ratio or anything else. If it is coefficient of artificial variable then this column will be zero.

step:-1

Given that

$m a x . P = 4 x + 2 y s u b j e c t t o, x + 2 y \leq 12 3 x + y \leq 21 x \geq 0, y \geq 0$

Let u, v be the slack variables, using in constraints to make them equations so we have

$x + 2 y + u = 12 3 x + y + v = 21$

Step:-2

So, the table is

B	$x_{B}$	x	y	u	v	Min. ratio
u	12	1	2	1	0	$\frac{12}{1} = 12$
v	21	3*	1	0	1	$\frac{21}{3} = 7$
P=0		4 $↑$	2	0	0

x will enter in the table and v will leave the table. So,

B	$x_{B}$	x	y	u	v	Min. ratio
u	5	0	$\frac{5}{3}$ *	1	$\frac{- 1}{3}$	$\frac{5 \times 3}{5} = 3$
x	7	1	$\frac{1}{3}$	0	$\frac{1}{3}$	$\frac{7 \times 3}{1} = 21$
P=28		0	$\frac{2}{3}$ $↑$	0	$\frac{- 4}{3}$

So, u will leave the table and y will enter the table,

Step:- 3

B	$x_{B}$	x	y	u	v
y	3	0	1	$\frac{3}{5}$	$\frac{- 1}{5}$
x	6	1	0	$\frac{- 1}{5}$	$\frac{2}{5}$
P=30		0	0	$\frac{- 2}{5}$	$\frac{- 6}{5}$

Hence, we have

Maximum P = $30$ , x= $6$ , y= $3$

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