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Ashok Kumar, Electrical Engineer
Category: Math Homework
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Experience:  Master's Degree
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Need some assistance answering some questions involving the

Customer Question

Need some assistance answering some questions involving the simplex method. I've been at this stuff for days now and my brain is fried.
Submitted: 1 year ago.
Category: Math Homework
Expert:  Ashok Kumar replied 1 year ago.

Thanks for requesting me. Kindly forward the questions.

Customer: replied 1 year ago.
Please see the attachment.
Expert:  Ashok Kumar replied 1 year ago.

Thanks. Kindly inform when these are due. It may take some time as I am on tour.

Customer: replied 1 year ago.
September 29, 2015 @ 11:59 PM CST
Expert:  Ashok Kumar replied 1 year ago.

How many hours from now?

Customer: replied 1 year ago.
roughly 12 hours from now. I have a huge time difference from where I am to the time zone they are due by.
Expert:  Ashok Kumar replied 1 year ago.

Answers are given in the attachment given below.

Kindly rate the answers. BONUS will be appreciated.

Expert:  Ashok Kumar replied 1 year ago.

Try the following link if above link is not opening.

Expert:  Ashok Kumar replied 1 year ago.
Customer: replied 1 year ago.
Can you explain why the statements are true or false?
Expert:  Ashok Kumar replied 1 year ago.

I will do it later today when I stop after traveling.

Customer: replied 1 year ago.
Great. I was able to get an extension. Thanks.
Customer: replied 1 year ago.
Just checking to see how things are going...
Expert:  Ashok Kumar replied 1 year ago.

I am back and will reply today.

Expert:  Ashok Kumar replied 1 year ago.

Please find attached herewith the link giving explanations.

Kindly rate the answers.

Customer: replied 1 year ago.
That link doesn't work for some reason.
Expert:  Ashok Kumar replied 1 year ago.

1. True or false: If all the coefficients ,,…, in the objective function P = + + … +arenonpositive, then the only solution of the problem is = = … = and P =0.

Let us havefollowing equation.

-2x1-3x2-4x3 = 0

We see that onlysolution for above equation is x 1=0, x2=0 and x3 =0 as variable values have tobe ≥0. Hence, given statement is true.

2. Trueor false: The pivot column of a simplex tableau identifies the variable whosevalue is to be decreased in order to increase the value of the objectivefunction (or at least keep it unchanged).

The simplex method is an iterative process. Starting atsome initial feasible solution (a corner point – usually the origin), eachiteration moves to another corner point with an improved (or at least notworse) value of the objective function. Iteration stops when an optimal solution(if it exists) is found. The value of the variable can beincreaesd also. Hence, given statement is false.

3. Trueor false: The ratio associated with the pivot row tells us by how much thevariable associated with the pivot column can be increased while thecorresponding point still lies in the feasible set.

This statement is true as we consider the lowest ratio for further iterations.

4. Trueor false: At any iteration of the simplex procedure, if it is not possible tocompute the ratios or the ratios are negative, then one can conclude that thelinear programming problem has no solution.

A linear programming will have no solution if the simplex method breaks down at somestage. For example, at some stage, there are no non-negative ratios in ourcomputations, and then the linear programming problem has no solution. Hence,statement is true.

5. Trueor false: If the last row to the left of the vertical line of the final simplextableau has a zero in a column that is not a unit column, then the linear programmingproblem has infinitely many solutions.

A linear programming problem will have infinitely manysolutions if, for example, the last row to the left of the vertical line of thefinal simplex tableau has a zero in a column that is not a unit column, or ifthe final tableau contains two or more indentical unit columns. Hence, givenstatement is true.

6. Trueor false: Suppose you are given a linear programming problem satisfying theconditions-

· Theobjective function is to be minimized.

· All thevariables involved are nonnegative, and

· Eachlinear constraint may be written so that the expression involving the variablesis greater than or equal to a negative constant.

Then the problem can be solved using thesimplex method to maximize the objective function P = -C.

These are the requirements of a linear programming problem to be solvedby simplex method. Hence, it is true.

7. Trueor false: The objective function of the primal problem can attain an optimalvalue that is different from the optimal value attained by the dual problem.

Primal and dual have samesolution; hence, given statement is false.

Expert:  Ashok Kumar replied 1 year ago.

Kindly rate the answers if no clarification is needed.