# 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.

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