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Assignment1Solution

# Assignment1Solution - Fall 2010 Optimization I(ORIE...

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Optimization I (ORIE 3300/5300) Assignment 1 Solution Problem 2 After reading pages 1-11 from the AMPL book, you noticed that the wine problem is just a special case of the production model, so we only need to construct the corresponding data ﬁle. Let’s start with the set of products. We have three products, the three types of wine: little red, Big Red, and AD White. So, the ﬁrst line of the data ﬁle will be: set P := lred BRed ADWhite; Now we have to specify, for each type of wine, three parameters: proﬁt (3, 4, and 5 dollars per bottle), maximum daily production (400, 300, and 200 bottles) and production rate (90, 80, and 60 bottles per hour). We can follow the original production data ﬁle to get: param: a c u := lred 90 3 400 BRed 80 4 300 ADWhite 60 5 200; The last parameter we have to deﬁne is the number of hours available for production: param b := 8; After saving the data ﬁle, we can run AMPL, read the model and data ﬁle, solve the problem and display the results: ampl: reset; ampl: model prod.mod; data plonk.dat; solve; display X; MINOS 5.5: optimal solution found. 3 iterations, objective 2447.5 X [*] := ADWhite 200 BRed 300 lred 82.5 ; So, the winery should produce 200 bottles of AD WHite, 300 bottles of Big Red, and 82.5 bottles of little red wine, for a total daily proﬁt of \$2447.50. Now, for Friday, the problem is a little bit diﬀerent; there are only 6 hours available. So, we change the parameter b from 8 to 6. We can do this by modifying plonk.dat; alternatively, we could leave plonk.dat unchanged, but type the following command: ampl: let b:= 6; . Then, we solve the modiﬁed problem and obtain a new solution: ampl: let b:= 6; ampl: solve; MINOS 5.5: optimal solution found. 2 iterations, objective 1875

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Assignment1Solution - Fall 2010 Optimization I(ORIE...

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