Thanks! Also @InteGrand, Wouldn't this be correct, I just formed this augmented matrix:
Reducing it to row echelon form:
But I didn't know what to do next.
As only the b column is non-leading there is a unique solution, so the possibility of having no solution is ruled out. However, the answers at the back say "Perhaps if the costs are negative or very large then you can be sure that someone is cheating". I get the bit about costs being negative thanks to your explanation, but what of the costs being very large?