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Linear Programming : Using the Simplex Method to Minimize C

In this problem I am trying to get rid of the artificial variable using the two phase method. However all of the rows either have negatives or zeros and my final answer keeps coming out to be a negative and none of the other answers plug into the constraints. The problem is

Using Simplex method minimize C:

C=15x1+12x2

Subject to 3x1+x2>18
x1+2x2<12
x1+x2=10
The numbers behind the x's are the sub numbers(x sub 1, x sub2, etc...)
The greater than and less than signs are also equal to(the 1st constraint is greater than or equal to)
My final answer for c = 144
Please help

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I cant get rid of the artificial variable in this problem using two phase method
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In this problem I am trying to get rid of the artificial variable using the two phase method. However all of the rows either have negatives or zeros and my final answer keeps coming out to be a negative and none of the other answers plug into the constraints. The problem is

Using Simplex method minimize C:

C=15x1+12x2

Subject to 3x1+x2>18
x1+2x2<12
x1+x2=10
The numbers behind the x's are the sub numbers(x sub 1, x sub2, etc...)
The greater than and less than signs are also equal to(the 1st constraint is greater than or equal to)
My final answer for c = 144
Please help

Optimal Solution: C= 144; x 1= 8, x2= ...

Solution Summary

The simplex method is employed to minimize a variable. The solution is detailed and well presented.

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