I am trying to write the solutions that can be read from each simplex tableau.
X1 x2 x3 s1 s2 s3 x
|0 2 0 5 2 2 0|15|
|0 3 1 0 1 2 0| 2|
|7 4 0 0 3 5 0|35|
|____________________________|
|0 -4 0 0 4 3 2|40|
How do I express the subscript numbers after X and the other numbers in the first row.
What is a simplex tableau?
I have no idea. I am taking classes on line and the book we are to follow explains nothing or it is off in other directions. Many students complain because some methods in the book no one has ever heard of
It is a cookbok method for finding the vertices and finding the max or min in a linear programming problem. Here is a link to how to set it up:
http://library.thinkquest.org/16500/FiniteMath/simplex.html
I also have never heard of this method
I did a Google search and one of the pages showed this
http://math.uww.edu/~mcfarlat/s-prob.htm
perhaps comparing what you have in your text with this might help
Thank you
Reiny
Went to both sites and yours was the easiest did the sample problem and came up with the right answer. I have problems with this class but thanks much.
In the given simplex tableau, the subscript numbers after X represent the variables in the linear programming problem. Each variable is denoted by its respective subscript number.
To interpret the given tableau, you need to understand the structure of a simplex tableau. Each column represents a variable, and each row represents a constraint or the objective function.
In the given tableau, the variables are:
- X1: Variable corresponding to the first column
- X2: Variable corresponding to the second column
- X3: Variable corresponding to the third column
- S1: Slack variable corresponding to the fourth column
- S2: Slack variable corresponding to the fifth column
- S3: Slack variable corresponding to the sixth column
- X: Artificial variable corresponding to the seventh column
The numbers in the first row represent the coefficients of the respective variables in the objective function. The objective function is usually placed in the bottom row (the one above the line).
In this case, the objective function is:
Z = 0*X1 + (-4)*X2 + 0*X3 + 0*S1 + 4*S2 + 3*S3 + 2*X
Here, the coefficients for each variable are:
X1: 0
X2: -4
X3: 0
S1: 0
S2: 4
S3: 3
X: 2
So, the expression for the objective function would be:
Z = -4X2 + 4S2 + 3S3 + 2X
I hope this helps you understand how to express the subscript numbers and coefficients in the first row of a simplex tableau. Let me know if you have any further questions!