3. Using AMPL to formulate and solve the MIP model

A chemical company annually produces 500 million pounds of the chemical maleic anhydride using four different reactors. Each reactor can be run in only one of the four settings. The following table gives the annual fixed cost (thousands of dollars), maximum production (in millions of pounds) and variable production cost (in thousands of dollars/million pounds) for each reactor and each setting. 4 160 Setting Fixed cost Max production Variable cost 1 70 75 0.09 1 55 60 0.14 4 150 190 0.09 205 0.06 Reactor 1 2 3 90 120 120 150 0.08 0.07 Reactor 3 2 3 100 140 140 175 0.10 0.9 Reactor 2 2 3 80 110 100 135 0.12 0.10 Reactor 4 2 3 70 90 90 110 0.15 0.15 Setting Fixed cost Max production Variable cost 1 80 90 0.10 4 180 225 0.11 1 40 50 0.15 4 110 150 0.12 Given that (1) a reactor can only be run on one setting for the entire year, (2) Reactor 4's setting could not be higher than Reactors 2 and 3's settings, and (4) Reactor 1 has the highest priority to be set up, how can the company meet its annual demand at minimum cost? 1. Write an optimization model for this problem. To receive full credit, your model should be algebraic. 2. Solve your model with Excel, and report the solution