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Expert: - 3/5/2010


Question
1)   Find out the optimal solution of the following LP problem through SIMPLEX method.
Maximize Z = 20x1  + 6 x2  + 8 x 3
Subject to
8 x1   +  2 x2   +  3 x3    %26#8804;  200
4 x1  +   3 x2                               %26#8804;  150
2 x1                           +   x3         %26#8804;     50
x1 ,  x2   and x3                      >  0

2)   Write dual of the problem given in Q.1. Explain the significance of dual variable in any LP problem.

3)   a) Explain the difference between pure strategy and mixed strategy.
b) How the concept of dominance is used in simplifying the solution of a  
   rectangular game?

4)   a) Discuss the parameters of Queing problem.   
b) Telephone department will install a second booth when convinced that an    
    arrival would expect to waiting for at least 3 minutes to get his chance. By how   
    much should be the flow of arrivals in order to justify a second booth. Length
    of phone call average is 3 min. Assume arrival and servicing rate as Poisson.

5)   Write short notes on the following
i)   Integer Programming
ii)   Dynamic Programming
iii)   Monte Carlo Simulation

Answer
1) Solved in attachment.
The variable to be added is in bold at the top,
the possible values are on the left side with the one chosen in bold,
the multiples to add to the other rows are in those rows,
the value to multiply the equation by with the left value in bod is in the same column,
slack variables are added in the 2nd and 3rd to the last columns,
and the solutions are in the last column.

The results say x1=50, x2=100/3, and the optimal value is 1,200.

2. The dual would have -150 -50 in the top row, and the inequalities would be
x+y>20, 3y>6, and x>8.

3a) Pure strategy is where only one method is used.
b) Mixed strategy is where more than one method is used.

4a) The main parameters are how often they arrive and how often they are served.
b) This depends on how fast people arrive and how fast they are served.

5i) An integer programming problem is any mathematical optimization or feasibility program in which some or all of the variables are restricted to be integral. In many settings the term integer program is used as short-hand for integer linear programming.

ii) Dynamic Programming is when you solve an optimization problem by caching subproblem solutions (memoization) rather than recomputing them.

iii) Monte Carlo methods are useful for modeling phenomena with significant uncertainty in inputs, such as the calculation of risk in business.

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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 even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. 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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