By Robert Fourer

AMPL is a language for large-scale optimization and mathematical programming difficulties in creation, distribution, mixing, scheduling, and lots of different purposes. Combining established algebraic notation and a strong interactive command setting, AMPL makes it effortless to create types, use a wide selection of solvers, and look at options. although versatile and handy for fast prototyping and improvement of versions, AMPL additionally deals the rate and generality wanted for repeated large-scale creation runs. This booklet, written through the creators of AMPL, is a whole consultant for modelers in any respect degrees of expertise. It starts with an educational on usual linear programming types, and provides all of AMPL's good points for linear programming with wide examples. extra chapters conceal community, nonlinear, piecewise-linear, and integer programming; database and spreadsheet interactions; and command scripts. such a lot chapters comprise workouts. obtain loose models of AMPL and several other solvers from www.ampl.com for experimentation, evaluate, and schooling. the website additionally lists owners of the industrial model of AMPL and various solvers.

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Kluwer Academic Publishers (Dordrecht, The Netherlands, 2001). An updated survey of linear programming theory and methods. 7 AMPL INTERFACES 21 Exercises 1-1. 2, but with a quite different story behind it. (a) You are in charge of an advertising campaign for a new product, with a budget of $1 million. You can advertise on TV or in magazines. 8 million potential customers; a magazine page costs $10,000 and reaches 1 million. You must sign up for at least 10 minutes of TV time. How should you spend your budget to maximize your audience?

A maximum of 120 minutes of radio? 1-2. The steel model of this chapter can be further modified to reflect various changes in production requirements. For each part below, explain the modifications to Figures 1-6a and 1-6b that would be required to achieve the desired changes. ) (a) How would you change the constraints so that total hours used by all products must equal the total hours available for each stage? Solve the linear program with this change, and verify that you get the same results.

Explain what happens when the available reheat time drops to 11 hours. 1-4. Here is a similar profit-maximizing model, but in a different context. An automobile manufacturer produces several kinds of cars. Each kind requires a certain amount of factory time per car to produce, and yields a certain profit per car. A certain amount of factory time has been scheduled for the next week, and it is desired to use all this time; but at least a certain number of each kind of car must be manufactured to meet dealer requirements.