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# Differential Equations/mathematics - basic simplex method

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Question
can you please tell me the steps involved in making the basic simplex tables for this question. ?
Maximize: Z = 15x1 +25x2
subject to : 5x1 +5x2 < equal to 25
10x1 + 15x2 < equal to 60
x1,x2 > equal to 0

(note - x is a variable. not the multiplication symbol)
thanks.

Answer
Sorry for the delay.
We take the coefficients, negate the Z row, and look for the greatest negative in the Z row.
We also add a slack variable for each of the equation.

The start of it is:
-15   -25
5     5   1   0   25
10    15   0   1   60

The entering variable would be x2, since -25 is more negative than -15.
This makes the column for x2 be the pivot column.
Now for the 1st equation, 25/5 = 5, and for the 2nd equation, 60/15 = 4.
Since 4 is smaller, so the 2nd equation is the pivot row.
This makes the 15 be the pivot element.

Since that's the pivot element, add  5/3 times the 2nd row to the Z row,
add -1/3 times the 2nd equation to the 1st equation,
and divide the 2nd equation by 15.

After only one iteration, that gives us
1.67   0   0    1.67   100
1.67   0   1   -0.33   5
0.67   1   0    0.07   4

Since there are no more negatives in the Z row, the optimum value has been achieved.

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#### Scott A Wilson

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I am capable of solving most ordinary differential equations and a few not so ordinary, but those are few and far between.

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