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# Advanced Math/MS-51 (Operations Research)

Question
Five employees of a company are to be assigned to five jobs, which can be done by any of them. The workers get different wages per hour. These are: Rs 5 per hour for A, B, and C each, and Rs 3 per hour for D and E each. The amount of time taken by each employee to do a given job is given in the following table. Determine the assignment pattern that (a) minimizes the total time taken, and (b) minimizes the total cost, of getting five units of work done.
Employee
Job   A   B   C   D   E
1   7   9   3   3   2
2   6   1   6   6   5
3   3   4   9   10   7
4   1   5   2   2   4
5   6   6   9   4   2

Operations Research
I did the calculations in Excel.
The sheet has been exported and attached.

The top row is the Z row where the least negative value is chosen.
The smallest negative value is chosen, and in this case, the one on the left.

The first column is the possible value if that row had the entering variable.
The smallest one is chosen, and then the pivot element is highlight.

The second column is what to multiply the pivot row by and subtract from the row it is in
if it is not the pivot row.  If it is, the value to multiply by to make the element a 1 is there.

There are no more negative values in the Z row, so after three iterations of the process,
we're done.

I just remembered how to attach files, so I send you a more readable copy.

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 9 Politeness = 10 Comment thank you very much for giving me the best solution sir

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#### Scott A Wilson

##### Expertise

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?

##### Experience

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.

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.

Past/Present Clients
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.