[Nightingale]

This is taken from the June 2007 paper, question 4 iii)
I am not able to follow the mark scheme at all and I don't know if I'm completely missing the point, because I initially thought the algorithm should have been two stage simplex due to the > constraint.
here's the question and I attached the solutions from the mark scheme. So it is just part iii) that I'm not understanding. If you can spot the link between the previous parts and this one please post a comment.


Noel is designing a hotel patio. It will consist of decking and paving.
Decking costs £4 per m2 and paving costs £2 per m2. He has a budget of £2500.
Noel prefers paving to decking, and he wants the area given to paving to be at least twice that given to decking.
He wants to have as large a patio as possible.
Noel’s problem is formulated as the following LP.
Let x be the number of m2 of decking.
Let y be the number of m2 of paving.

(i) Use the simplex algorithm to solve this LP. Pivot first on the positive element in the y column.

Noel would like to have at least 200m2 of decking.
(ii) Add a line corresponding to this constraint to your solution tableau from part i), and modify the resulting table either for two-stage simplex or the big-M method. Hence solve the problem.

Noel finally decides that he will minimise the annual cost of maintenance, which is given by subject to the additional constraint that there is at least 1000 m2 of patio.

(iii) Starting from your solution to part (ii), use simplex to solve this problem.

[Coursework.info]

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[hayzelle]

I'm stuck with the exact same bit, the solution seems to make no sense!