D2 June 2013 (R) Q5

EdexcelOld spec8 marksLinear Programming

5. A three-variable linear programming problem in \(x\), \(y\) and \(z\) is to be solved. The objective is to maximise the profit, \(P\).

The following tableau is obtained.

Basic variable\(x\)\(y\)\(z\)\(r\)\(s\)\(t\)Value
\(r\)\(\frac{1}{2}\)\(-\frac{1}{2}\)010\(-\frac{1}{2}\)10
\(s\)\(1\frac{1}{2}\)\(2\frac{1}{2}\)001\(-\frac{1}{2}\)5
\(z\)\(\frac{1}{2}\)\(\frac{1}{2}\)100\(\frac{1}{2}\)5
\(P\)–5–1000020220
(a) Starting by increasing \(y\), perform one complete iteration of the Simplex algorithm, to obtain a new tableau, T. State the row operations you use. (5)
(b) Write down the profit equation given by T. (1)
(c) Use the profit equation from part (b) to explain why T is optimal. (2)
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