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Question
1. Solve the following LP problem using SIMPLEX method
  MINIMIZE     Z = 5X1 - 2X2 +3X3

  Subject to
         2X1 + 2X2  - X3  >= 2
         3X1 4X2        <= 3
         X2  + 3X3  <= 5

       X1 , X2  and X3  >= 0

2.a) Write the DUAL of the LP problem given the Problem - 1 and find out the solution of Dual problem from the final table of simplex (Primal).
(b) Discuss the differences between PRIMAL and DUAL.
(C) Explain  the economic interpretation of DUAL variable.

Answer
The 1st constraint has a greater than or equal to sign rather than a less then or equal to,
so bring in the smallest value from the z-row to find which row to add.

The Z-row would have a -5 2 -3, so X3 would be the entering variable.
Constraint #3 is the only one with a positive value in that column,
so use X3 as the entering varialbe.

Add -1/3 * C3 to the Z row and C1, leave C2, and divide C3 by 3.
This should give the next tableau. Once this has been gotten to,
use X1 as the entering basic variable in constraint 3.

This should have x3 as 5/3, which satisfies the 1st constraint.
The 2nd constraint isn't satisfied yet, so keep trying to minimize the answer.

The next element to add would be x1, using row 3.
Once this has been done, the Z row has all positive coefficients and
the 1st constraint is satisfied, so the problem is done.

It should look like
-5    2   -3   0    0   0   0   0
2    2   -1   1   -1   0   0   2
3   -4    0   0    0   1   0   3
1    0    3   0    0   0   1   5
         
-4    2   0   0    0   0   1   5
2.3333    2   0   1   -1   0   0.3333   3.6667
3   -4   0   0    0   1   0   3
0.3333    0   1   0    0   0   0.3333   1.6667
         
0    2   12   0    0   0    5    25
0    2   -7   1   -1   0   -2    -8
0   -4   -9   0    0   1   -3   -12
1    0    3   0    0   0    1     5

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for over two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

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My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.

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