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# find the z or maximum or optimum using the simplex method in tabular form: Maximize:...

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find the z or maximum or optimum using the simplex method in tabular form:

Maximize: z=2x + 3y -t

subject to: x + 3y + 4t ≤ 12

x + y + 2t ≤ 18

2x - y - t ≤ 16

x≥ 0, y≥ 0, t≥ 0

New Linear programming w/ slack variables

Max: z=2x + 3y - t

subject to: x + 3y + 4t + u = 12

x + y + 2t         + v = 18

2x - y - t               +w = 16

initial feasible sol'n:

x= 0, y = 0, t=0, u=12, v = 18, w=16

Posted by bluecute on April 18, 2013 at 2:15 PM via web and tagged with math, the simplex method in tabular form

We have t oset this condition: Colled `r_1,r_2,r_3`  the rows  subjecting:

`ar_1+br_2+cr_3=z`

that means:

`ax+bx+2cx=2x`

`3ay+2by-cy=3y`

`at+2bt-ct=-t`

it gives us a sistems in unknows a,b,c.

`Delta=[[1,1,2],[3,2,-1],[1,2,-1]]` `=14`

`Delta_a=[[2,1,2],[3,2,-1],[-1,2,-1]]` `=28`

`Delta_b=[[1,2,2],[3,3,-1],[1,-1,-1]]` `=-6`

`Delta_c=[[1,1,2],[3,2,3],[1,2,-1]]` `=10`

We get:

`a= Delta_a/Delta=2`        `b=Delta_b/Delta=-3/7`     `c=Delta_c/Delta=5/7`

So:

`z=2r_1-3/7r_2+5/7r_3`

That means:

`z<= 2(12)-3/7(18)+5/7(16)` `=142/7`

Posted by oldnick on April 18, 2013 at 3:59 PM (Answer #1)