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Differential Equations/mathematics - basic simplex method


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)

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


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


I have taken Differential Equations at OSU. Occasionally I have assisted people with questions on the subject.

I wrote a thesis on the study of shock waves and rarefaction fans. That occurs in nature when mathematics fails to apply. See, mathematics says that when shock waves appear, there should be two solutions whereas nature knows there is only one way to be in that area. When rarefaction fans occur, the mathematics says there should be no solution, but despite this, nature still moves ahead with its own plan.

I received an MS degree at OSU in Mathemematics and a BS degree at OSU in Mathematical Science.

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I graduated from OSU with a Bachelor of Science degree in mathematics with honors. Two years later, I graduated from OSU with a Master of Science degree in mathematics with honors. Between these two degrees, I have more hours in graduate courses that required to get them.

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I answered many questions at OSU, down in south seattle at a college, at a church in Corvallis, OR, as Safeway in Washington, and many other areas. I have answered over 8,500 right here, but only a little over 190 of them have been in differential equations.

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