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

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.

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Input $10P$ as your answer.

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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.

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This is part of the set OCR A Level Problems .