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Examen 1 DMT - (Spring 2013) Instrucciones: Format: Times New Roman, 12pts, 1.5" space, 1" margin (all around), Full Justification, English...

This question was answered on Apr 21, 2013. View the Answer
La Refinería Azteca produce dos tipos de gasolina sin plomo, regular y extra los cuales
vende a su cadena de estaciones de servicio en $12 y $14 por barril, respectivamente.
Ambos tipos se preparan del inventario de la Azteca de petróleo nacional refinado y de
petróleo importado refinado, y deben cumplir con las siguientes especificaciones:

Presión Octanaje Demanda Entregas
maxima Minim0 máxima, j minimas
de vapor barriles/ barriles/
semana semanas.
Regular 23 88 100000 50000
Extra 23 93 20000 5000

Las características del inventario de petróleos refinados son las siguientes:

Presión Octanaje Inventario Costo
de vapor barriles S/barril

Nacional 25 87 40000 8
Importado 15 98 60000 15

1.¿Qué cantidades de los dos petróleos (nacional e importado) deberá mezclar la Azteca en
ambas gasolinas, a fin de maximizar la ganancia semanal?

2.¿Si la Refinería Azteca tuviese la potestad de pagar cualquier cantidad por barril del petróleo nacional (políticas proteccionistas, etc.), cuanto es el máximo que la empresa debería estar dispuesta a pagar por un barril adicional?
Exercise # 1 (R).pdf

Examen 1 DMT - (Spring 2013)
Instrucciones: Format: Times New Roman, 12pts, 1.5” space, 1” margin (all around),
Full Justification, English or Spanish, Name & Student Number on the
upper right corner of first page, send it as a PDF file. Don’t write the Question. Just your answers in a statement form. Maximum of four pages. Due Time: Sunday 21, 09:30PM. NO EXCEPTION. Those received
after this time, the student(s) will receive an Incomplete. Two or more tests that equitable resemble eac h other will receive
zero. When you send your test, write DMTTEST1 in the message subject. Each violation of these instructions will have a 5% deduction, from
the total scored.
Situación 1 1. ¿Qué cantidades de los dos petróleos deberá mezclar la Azteca en amabas
gasolinas, a fin de maximizar la ganancia semanal y cuánto sería esa ganancia? 2. ¿Si la Refinería Azteca tuviese la potestad de pagar cualquier cantidad por barril del
petróleo nacional (políticas proteccionistas, etc.), cuanto es el máximo que la
empresa debería estar dispuesta a pagar por un barril adicional? Situación 2.
La Asociación de Industriales de Puerto Rico periódicamente promueve servicios
públicos, seminarios y programas. Actualmente los planes de promoción para este año
están en marcha. Los medios alternativos para realizar la publicidad así como los
costos y la audiencia estimados por unidad de publicidad, además de la cantidad
máxima de unidades de publicidad en que puede ser usado cada medio , se muestra a
Audiencia por unidad de
Costo por unidad de
Uso máximo del medio Televisión
123,000 Radio
21,000 Prensa
51,000 $5,000 $900 $1,200 6 12 15 Para lograr un uso balanceado de los medios, (1) la publicidad en radio no debe
exceder el 60 por ciento del total de unidades de publicidad autorizada s, (2) la cantidad
de unidades autorizadas en televisión debe ser al menos 15 por ciento del total
autorizado en los medios, (3) el presupuesto total para promociones se ha limitad o a
$25,000 y (4) la publicad en Radio tiene que ser cinco veces la de Televisión.
a) ¿Cómo se puede maximizar la audienci a total?
b) Explique tres suposiciones claves en que se basa su modelo. Situación 3. Situación 4.
An important skill in model formulation is the ability to enumerate all alternatives. Scott
Wilkerson is a scientist-astronaut aboard a seven-day space shuttle mission. In spite of
a modest health problem that is aggravated by the zero gravity of space, Sc ott has been
allowed on the mission because of his scientific skills and because a pharmaceutical
company has prepared a set of two types of pills for Scott to take each day to alleviate
his medical condition. At the beginning of each day Scott is to take exactly one type X
pill and exactly one type Y pill. If he deviates from this scheme, it will be life threatening
for him and the shuttle will have to be brought down immediately. On the first day of the
mission, Scott gets one type X pill out of the X bottle, but in the process of trying to get a
pill out of the Y bottle, two come out. He grasps for them immediately with the hand that
has the X pill and now he finds he has three pills in his hand. Unfortunately, the X and Y
pills are indistinguishable. Both types look exactly like a standard aspirin. There are just
enough pills for the full length mission, so none can be discarded. What should Scott
do? (Hint: this problem would be inappropriate in the integer programming chapter.) Situación 5.
The Tiny Timber Company wants to utilize best the wood resources in one of its forest
regions. Within this region, there is a sawmill and a plywood mill. Thus, timber can be
converted to lumber or plywood. Producing a marketable mix of 1000 board feet of
lumber products requires 1000 board feet of spruce and 4000 board feet of Douglas fir.
Producing 1000 square feet of plywood requires 2000 board feet of spruce and 4000
board feet of Douglas fir. This region has available 32,000 board feet of spruce and
72,000 board feet of Douglas fir. Sales commitments require at least 5000 board feet of
lumber and 12,000 square feet of plywood be produced during the planning period. The
profit contributions arc $45 per 1000 board feet of lumber products and $60 per 1000
square feet of plywood. Let L be the amount (in 1000 board feet) of lumber produced
and let P be the amount (in 1000 square· feet) of plywood produced. Express the
problem as a linear programming model. Situación 6.
PRComputers makes quarterly decisions about their product mix. While their full
product line includes hundreds of products, we will consider a simpler problem with just
two products: notebook computers and desktop computers. PRComputers would like to
know how many of each product to produce in order to maximize profit for the quarter.
There are a number of limits on what PRComputers can produce. The major constraints
are as follows:
o Each computer (either notebook or desktop) requires a Processing Chip. Due to
tightness in the market, our supplier has allocated 10,000 such chips to us.
o Each computer requires memory. Memory comes in 16MB chip sets. A notebook
computer has 16MB memory installed (so needs 1 chip set) while a desktop
computer has 32MB (so requires 2 chip sets). We received a great deal on chip
sets, so have a stock of 15,000 chip sets to use over the next quarter.
o Each computer requires assembly time. Due to tight tolerances, a notebook
computer takes more time to assemble: 4 minutes versus 3 minutes for a
o There are 25,000 minutes of assembly time available in the next quarter. Given
current market conditions, material cost, and our production system, each
notebook computer produced generates $750 profit, and each desktop produces
$1000 profit.
There are many questions PRComputer might ask. The most obvious are such things
as “How many of each type computer should PRComputer produce in the next
quarter?", “What is the maximum profit PRComputer can make?" Less obvious, but
perhaps of more manageri al interest are “How much should PRComputer be willing to
pay for an extra memory chip set?" “What is the effect of losing 1,000 minutes of
assembly time due to an unexpected machine failure?", “How much profit would we
need to make on a 32MB notebook comp uter to justify its production?". W hat do you
suggest? Situación 7.
Carmen, the manager of a department store in Puerto Rico, is attempting to decide on
the types and amounts of advertising the store should use. She has invited
representatives from a local radio station, a television station, and a newspaper to make
presentations in which they describe their audiences. The television station
representative indicates that a TV commercial, which costs $2 5,000 per spot, would
reach 35,000 potential customer s. The newspaper representative claims to be able to
provide an audience of 10,000 potential customers at a cost of $4,000 per ad. The radio
station representative says that the audience for one of the station’s commercials, which
costs $5,000 per spot, is 15,000 customers. The breakdown of the audience (in
thousands) is as follows. Senior
Young Television
5 7 Newspaper
4 3 Male
7 Radio
2 The store has the following advertising policy: Use at least twice as many radio commercials spots as newspaper ads and tv
commercial spots, combined.
Reach at least 100,000 customers.
Reach at least twice as many young people as senior citizens.
Make sure that at least 30% of the total audience is fema le. Available space limits the number of newspaper ads to seven. Carmen wants to know
the optimal number of each type of advertising to purchase. Situación 8.
R.T. produces two telephone models, each of which must go through three workstations
for manufacturing, assembly, and quality cont rol. At this time, the company is deciding
between two Assembly processes, and only one of the Processes (1 or 2) will be used.
The amount of time required for each model in each of the work areas is given in the
following table. Model Manufacturing Standard 7 minutes
Trimline 2 minutes Assembly
Process 1
5 minutes 2 minutes
4 minutes 5 minutes Quality
2 minutes
3 minutes

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P x1 x2
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This question was asked on Apr 20, 2013 and answered on Apr 21, 2013.

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