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Hi Scott plz help me with answer to these questions:-
1) Discuss the principles of modelling in Operations Research. Identify the application of
O.R. in manufacturing and service sectors.
2) Solve the following linear programming problem through simplex method
Minimize Z = 600 x1 + 500 x2
Subject to
2x1 + x2 > 80
x1 + 2x2 > 60
x1,x2 > 0
3) a) Explain the Primal – Dual relationship.
b) What is the significance of dual variable in LP – Problem.
4) a) Explain MAXIMIN and MINIMAX criteria in Game Theory.
b) Explain saddle point, pure and Mixed Strategy.
5) In a bank there is only one window, a solitary employee performs all the services required
and window remains continuously open from 7 AM to 1 PM. It has been discovered that the
average number of clients are 54 during the day and that the average service items in of five
minutes per person. Calculate
a) The average number of clients in the system
b) The average waiting time
c) The utilization rate of the window
6) Write short notes on
a) Goal Programming
b) Dynamic Programming
1. Operations research assumes that each item has a cost per unit.
It assumes the cost is linear. It ignores any base costs.
2. Since it is a maximize problem, do the dual as a simple OR problem. That's let x = 80t1 + 60t2 subject to the constraints
2t1 + t2 <= 600 and t1 + 2t2 <= 500.
3. The problem must be in the form with all of the variables >= 0,
all of the equation >= constant. The constraint go in the Z row.
What is in the Z row becomes the constraints. Each equation becomes
a column in the dual problem. The solutions for the dual problem is the same as the coefficients for the slack variables in the primal problem.
4. From what I remember, The maximin maximizes the minimum amount won. The minimax minimizes the amount lost. A saddle point is when both oppenets reach the same conclusion about which way to go.
A good paper on the minimax is http://www.geocities.com/arufast/a03minimax.html
A good paper on saddle points is
http://www.mathpsyc.uni-bonn.de/doc/micko/2c.htm
5) That's 54 people per 6 hours.
The number being seriveced at any time is a Poisson distribution
with lambda = 50 customers/6 hours.
The time between services is an exponential distribution.
The utilization rate is 270/360 = 3/4.
Here is a good on goal programming.
http://en.wikipedia.org/wiki/Goal_Programming
Here is a goot one on dynamic programming.
http://en.wikipedia.org/wiki/Dynamic_programming
With a little reading, these questions shouldn't be too hard to answer.
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Answers by Expert:
Scott A Wilson
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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.
Publications
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.
Education/Credentials
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.
Awards and Honors
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 nearby, friends with math questions,
and several people every day on the PC, and you're probably make one more.
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