How to Carry out the Simplex Algorithm
First you need to look at what you're trying to work out., Once you have these you need to introduce slack variables into the inequalities., The constraint should be in the form P=x+y(+z) which you need to rearrange to become 0=P-x-y(-z)., Once you...
Step-by-Step Guide
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Step 1: First you need to look at what you're trying to work out.
Do you already have the function you are maximising/minimising and the constraint inequalities? , Slack variables turn inequalities into equations and usually use the letters s onwards (though you can use any letter you like), for example: 2y+4x<=8 becomes 2y+4x+s=8 6y+2x<=28 becomes 6y+2x+t=28 , for example:
P=2x+2y becomes 0=P-2x-2y , This is constructed as follows:, Your first row will be what you are maximising, the rows below the constraints.
If you have that letter in wat goes in that row the number goes into that column.
If the letter is not there put a
0., Pick a column, any column, so long as the top number is negative (please note that you can't use l) For the sake of the example I'm going to use x, but if you're bored you can use y just to be different (if you have a lot of columns to choose from I'd recommend starting at the left, makes life easier).
For each row (for which the number in your chosen column is positive) divide the number in the l column by the number in your chosen column.
For the row which gave the smallest value, ring the number in your chosen column. (In my example it would be 4) This number is called the pivot. , Leave a line for equation 4 and divide (2) by the pivot (in this case 4) then write that into the space for (5), You do this by combining appropriate multiples of the pivot with the original equation for each line.
For example (4)=(1)+0.5(2) Once you have done this your tableau should look like this:, Once this is the case you have completed your simplex problem., Ignore the slack variables.
The last (l) column (of the final iteration) contains the values for the function (P) and non-zero variables. -
Step 2: Once you have these you need to introduce slack variables into the inequalities.
-
Step 3: The constraint should be in the form P=x+y(+z) which you need to rearrange to become 0=P-x-y(-z).
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Step 4: Once you have your data you need to construct the tableau.
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Step 5: You then need to put your data into the tableau.
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Step 6: Now the fun bit.
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Step 7: At this point you need to draw a line in your tableau so you can write in the first iteration.
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Step 8: You now need to make all the values in the x column (apart from your pivot line) equal to 0.
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Step 9: If you still have negative numbers on your top row (not including column l) repeat steps 6-8 until all your top row are positive.
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Step 10: You read the solution of your simplex problem very simply.
Detailed Guide
Do you already have the function you are maximising/minimising and the constraint inequalities? , Slack variables turn inequalities into equations and usually use the letters s onwards (though you can use any letter you like), for example: 2y+4x<=8 becomes 2y+4x+s=8 6y+2x<=28 becomes 6y+2x+t=28 , for example:
P=2x+2y becomes 0=P-2x-2y , This is constructed as follows:, Your first row will be what you are maximising, the rows below the constraints.
If you have that letter in wat goes in that row the number goes into that column.
If the letter is not there put a
0., Pick a column, any column, so long as the top number is negative (please note that you can't use l) For the sake of the example I'm going to use x, but if you're bored you can use y just to be different (if you have a lot of columns to choose from I'd recommend starting at the left, makes life easier).
For each row (for which the number in your chosen column is positive) divide the number in the l column by the number in your chosen column.
For the row which gave the smallest value, ring the number in your chosen column. (In my example it would be 4) This number is called the pivot. , Leave a line for equation 4 and divide (2) by the pivot (in this case 4) then write that into the space for (5), You do this by combining appropriate multiples of the pivot with the original equation for each line.
For example (4)=(1)+0.5(2) Once you have done this your tableau should look like this:, Once this is the case you have completed your simplex problem., Ignore the slack variables.
The last (l) column (of the final iteration) contains the values for the function (P) and non-zero variables.
About the Author
Michelle Hamilton
Dedicated to helping readers learn new skills in creative arts and beyond.
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