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Solve LP using the Simplex Method

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State all the assumptions and show all the work. Define your decision variables clearly. Briefly explain the constraints and objectives functions and define all unit of measure.

Consider the following linear programming problem:

Max x + 3y
s.t. -x + y < 2
x + 3y < 21
x - y < 3
x > 0
y > 0

a) Solve LP using the Simplex Method. What is the optimal solution? What is the optimal objective function value?
b) Plot the feasible region. Label (in order) the corner points you visited during the simplex method. What is the basic feasible solution at each of these points?
c) Add the constraint x + y > 1 to the LP problem. Set up the initial tableau for this new problem and perform one full iteration of the simplex method (See attached in the file).

Will appreciate your support on this.

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Linear programming using two-phase simplex and graphical method

a) When solving linear programming problems a number of problem cases can arise. Explain, with the aid of diagrams where appropriate, how you would identify each of the following cases when solving a two-variable problem using the graphical method and when using the two-phase Simplex method.

i) A non-unique solution
ii) An infeasible problem.
iii) An unbounded problem.
iv) A degenerate solution.
v) Describe the usual consequence of degeneracy and explain briefly how degeneracy can be avoided.

b) Explain how the two-phase Revised Simplex method indicates that a linear programming problem is (i) infeasible, (ii) unbounded and (iii) has infinitely many solutions.

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