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UNIVERSIDAD DISTRITAL FRANCISCO JOS DE CALDASPROYECTO CURRICULAR DE INGENIERIA INDUSTRIAL - REA OPERACIONES Y LOGSTICAPROGRAMACIN NO LINEAL. Cdigo: 182. Crditos: 2.Profesor: M.Sc. Eduyn Ramiro Lpez Santana (erlopezs@udistrital.edu.co )Actualizado: martes, 13 de agosto de 2013

TALLER 1

Reglas de Entrega

Fecha de entrega: lunes 26 de agosto. Saln de clase (entrega taller impreso). El taller ser realizado en grupos de 3 personas.

La solucin de cada uno de los problemas que se enuncian a continuacin debe contener:

o Breve descripcin del problema (caractersticas, supuestos, etc.)

o Formulacin matemtica

o Sntesis de resultados

o Conclusiones

o Anexos (modelos en el software seleccionado, salidas y toda la informacin de soporte que sustente

su trabajo) deben ser ingresados en el link de l aula virtual llamado Taller 1, hora lmite 7:00am dellunes 26 de agosto de 2013.

Una sola carpeta comprimida

Nombre: PNL-2013-2_T1_GRUPO (21 o 23)_CODIGOS.

Solo debe ser cargado por uno de los integrantes del grupo.

o Los anexos deben ser citados en el contenido del documento, y deben ejecutarse de forma adecuada.

o Solo se tendr en cuenta los archivos ingresados al link.

o El taller es sujeto a sustentacin.

El reporte debe ser conciso y preciso.

El informe debe ser presentado segn el formato de presentacin de artculos de la Revista de Ingeniera de la

Universidad Distrital, siguiendo todas las normas de publicacin de la misma. El reporte debe entregarse impreso en la fecha especificada y adems debe estar junto con los anexos

(carpeta comprimida). Debe entregarlo marcado con el cdigo y nombre de los integrantes del grupo yespecificar quien subi los archivos de soporte al aula virtual (impreso por ambas caras de la hoja).

Recuerde que cualquier trabajo entregado/enviado despus de la fecha y hora lmite no se tendr en cuenta.

Cualquier intento de copia ser reportado de acuerdo al reglamento de la Universidad.

Debe colocar la siguiente informacin en la primera pgina:

Cdigo Nombre% Participacin en el

trabajo / 100%Nota

1.

2.3.

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Problema 1

Use the one-dimensional search procedures (at least four procedures) to interactively solve (approximately) the

following problems:

a) Maximize() . Use an error tolerance and initial bounds

b) Maximize() with , and tolerance c) Minimize () , Use an error tolerance and find appropriate initial

bounds by inspection.

d) Maximize () Use an error tolerance and find appropriateinitial bounds by inspection.

Problema 2

Suppose that in at bats, a baseball player gets hits. Suppose we want to estimate the players probability ()of getting a hit on each at bat. The method of maximum likelihood estimates by , where maximizes the

probability of observing hits in at bats. Show that themethod of maximum likelihood would choose .

Problema 3

During the Reagan administration, economist Arthur Laffer became famous for his Laffer curve, which implied

that an increase in the tax rate might decrease tax revenues, while a decrease in the tax rate might increase tax

revenues. This problem illustrates the idea behind the Laffer curve. Suppose that if an individual puts in a degree

of effort , he or she earns a revenue of 10. Also suppose that an individual associates a cost of with aneffort level of . Suppose further that the tax rate is . This means that each individual gets to keep a fraction of before-tax revenue. Show that maximizes the governments tax revenues. Thus, if the tax rate

were 60%, then a cut in the tax rate would increase revenues.

Problema 4

It costs $250 to produce an X-Box. We are trying to determine the selling price for the X-Box. Prices between $200

and $400 are under consideration, with demand for prices of $200, $250, $350, and $400 given below. Suppose

MSFT earns $10 in profit for each game that an X-Box owner purchases. Determine the optimal price and

associated profit for the case in which an average X-Box owner buys 10 games.

Console Price ($) Demand200 2.00E_06

250 1.20E_06

350 6.00E_

05

400 2.00E_05

Unit cost $250

Problema 5

Suppose a company must service customers lying in an area of sq mi with warehouses. Kolesar and Blumhave shown that the average distance between a warehouse and a customer is . Assume that it costs the

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company $60,000 per year to maintain a warehouse and $400,000 to build a warehouse. (Assume that a $400,000

cost is equivalent to forever incurring a cost of $40,000 per year.) The company fills 160,000 orders per year, and

the shipping cost per order is $1 per mile. If the company serves an area of 100 sq mi, then how many warehouses

should it have?

Problema 6Hughesco is interested in determining how cutting fluid jet pressure () affects the useful life of a machine tool(), given below. Pressure is constrained to be between 0 and 600 pounds per square inch (psi). Use GoldenSection Search to estimate (within 50 units) the value of that maximizes useful tool life. Assume that is aunimodal function of .

(Pounds per Square Inch) (Minutes)229 39

371 81

458 82

513 79

425 84

404 85

392 84

Problema 7

Oilco produces three types of gasoline: regular, unleaded, and premium. All three are produced by combining

lead and crude oil brought in from Alaska and Texas. The required sulphur content, octane levels, minimum

daily demand (in gallons), and sales price per gallon of each type of gasoline are given in Table 3. The crude

brought in from Alaska is made by blending two types of crude: Alaska1 and Alaska2. The Alaska crude is

blended in Alaska and shipped via pipeline to Oilcos Texas refinery. At most, 10,000 gallons ofcrude per day can

be shipped from Alaska. The sulphur content, octane level, daily maximum amount available (in gallons) andpurchase cost (per gallon) for each type of Alaska crude, Texas crude, and lead are given in Table 4. Of course,

unleaded gasoline can contain no lead. Formulate an NLP (non-linear problem) to help Oilco maximize the daily

profit obtained from selling gasoline.