# 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.**