OCR A Level: Decision 1 - Simplex [June 2012 Q4]

Computer Science Level pending

Consider the following linear programming problem.

\((\text{i})\) Use slack variables \(s\), \(t\) and \(u\) to rewrite the first three constraints as equations. What restictions are there on the slack variables?

\((\text{ii})\) Represent the problem as an initial Simplex tableau.

\((\text{iii})\) Show why the pivot for the first iteration of the Simplex algorithm must be the coefficient of \(z\) in the third constraint.

\((\text{iv})\) Perform one iteration of the Simplex algorithm, showing how the elements of the pivot row were calculated and how this was used to calculate the other rows.

\((\text{v})\) Perform a second iteration of the Simplex algorithm and record the values of \(x\), \(y\), \(z\) and \(P\) at the end of this iteration.

\((\text{vi})\) Write down the values of \(s\), \(t\) and \(u\) from your final tableau and explain what they mean in terms of the original constraints.

Input \(10P\) as your answer.

There are 2 marks available for part (i), 2 marks for part (ii), 2 marks for part (iii), 3 marks for part (iv), 3 marks for part (v) and 2 marks for part (vi).
In total, this question is worth 19.4% of all available marks in the paper.

This is part of the set OCR A Level Problems.

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