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# Surfboard Production Problem

Just wondering if I got the gist of the expert problem.

We are going to keep prices fixed at the optimal solution produced by the non-linear solution? If this is not the case, then I think most of us have miss understood what is needed to do this problem.

If this is the case, then won't it be much easier to graphically diplay the infomation in MATLAB, or is there a simple way in AMPL (the problem states use AMPL and CPLEX).

-- TWikiGuest - 24 Mar 2008

For the expert problem you should fix the Price values using a loop (as shown in the Extra for Experts section). Then the problem becomes a mixed integer programme and can be solved using CPLEX to find the optimal production amounts and (more importantly) the optimal profit.

Then you simply need to plot the surface showing how the optimal profit changes with the prices of the Malibu and Super Thruster surfboards respectively. This will show if the answer from MINLP is the global maximum.

-- MichaelOSullivan - 24 Mar 2008

By using the loop you are trying different pairs of prices (varying between 1 and 150) for the Malibu and Super Thruster. For example, when p = 100 and q = 25 the price is \$100 for a Malibu board and \$25 for a Super Thruster board. CPLEX will then find the optimal production amounts for these prices, giving the optimal profit and hence the objective for these prices. By looking at all values in the loop we are seeing how the objective function value changes for all the different price combinations.

-- MichaelOSullivan - 24 Mar 2008

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