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Shortest paths-Simplex Method confusion watch

1. If anyone has the OCR D1 book, it's on p105.

So, I'm meant to find the shortest path from A to C, which should be amazingly easy, except I'm clearly missing something.

The problem involves a triangularly shaped network with sides a, b and c
and it's aim comes down to minimizing a+5b+3c

But if you're minimizing it, you're maximizing it's negative, hence;
-P=a+5b+3c
which as P+a+5b+3c=0, seems to already be in it's final form- all the coefficients in what would be the top column of the tableau are positive.

Yet it's minimum is clearly not 0, but 4 and can be achieved by a=1, b=0 and c=1

Help?
2. The book uses it as an example, but expects people to be able to work certain bits out themselves (which sadly include this)

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Updated: November 14, 2013
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