cyeokpeng

The admissions office at State University wants to develop a planning model for next year's entering freshman class. The university has 4500 available openings for freshmen. Tuition is $8600 for a local student, and $19200 for an overseas student. The university wants to maximize the tuition fees it receives new year. By state mandate, it can admit no more than 47% overseas students. Also, each college in the university must have at least 30% local students in its freshmen class.

In order to be ranked in several national magazines, it wants the freshmen class to have an average SAT score of 1150. Following are the average SAT scores for last year's freshmen class for local and overseas students in each college in the university plus the maximum size of the freshmen class for each college:

College Local (SAT) Overseas (SAT) Total Capacity

1. Architecture 1350 1460 470

2. Arts and Social Sciences 1010 1050 1300

3. Agriculture 1020 1110 240

4. Business 1090 1180 820

5. Engineering 1360 1420 1060

6. Human Resources 1000 1400 610

Ans: (Textbook question, but no answers)

I show some of the workings, not all because too tedious:

Let the decision variables be xj = no. of students as shown in the table below

College Local Overseas

1. Architecture x1 x2

2. Arts and Social Science x3 x4

3. Agriculture x5 x6

4. Business x7 x8

5. Engineering x9 x10

6. Human Resources x11 x12

Objective Function

Maximize tuition fees,

Z = $ 8600x1 + 19200x2 + 8600x3 + 19200x4 + 8600x5 + 19200x6

+ 8600x7 + 19200x8 +8600x9 + 19200x10 + 8600x11 + 19200x12

Subject to:

Class size constraints for each college is straightforward, there are 6 of them, with total no. of students in that college <= stated class size.

The two state policies are also straightforward, so I don't waste time showing.

I only have problems in the last type of constraints i.e. the constraints relating to the average SAT scores.

The constraints talk about each of the class must have an average SAT score of 1150. We are only given past year average SAT scores for each local and overseas student in each type of college. Question is: with only these limited info, how are we going to model these constraints?

I tried this way of modeling the average SAT score constraints, but it gives me with some problems too.

Using past year SAT scores to model this year scores (assume),

(Estimated total scores for local students in certain college*no. of local students +

Estimated total scores for overseas students in same college*no. of overseas students) / total no. of students in that college ≥ 1150

Hence, there will be 6 constraints for 6 different colleges!

But after some algebraic manipulations, some constraints seem to be nonsensical.

Eg. −200x1−310x2 ≤ 0 (always true, so can delete)

140x3 + 100x4 ≤ 0 (always false)

130x5 + 40x6 ≤ 0 (always false)

60x7 − 30x8 ≤ 0 (this constraint is ok)

−210x9−270x10 ≤ 0 (always true, so can delete)

150x11 − 250x12 ≤ 0 (this constraint is ok)

Can I make some reasonable assumptions to solve this problem?

Like, since in the Arts & Social Sciences college and Agriculture college, it is impossible to make the average SAT score to meet minimum standards, so we leave it out of the constraints.

i.e. the constraints (using those with physical meaning) for these become:

60x7 − 30x8 ≤ 0

150x11 − 250x12 ≤ 0

Is there any logical error behind this reasoning and assumptions?

I am at a loss of how to write down circuit network equations when

(i) a current source which cannot be clearly converted into a equivalent

voltage source is included in one specific mesh.

(ii) a dependent voltage source is included in one specific mesh.

using the matrix equation form.

For (i), the voltage across the current source is dependent on the variables of mesh currents, so it cannot be included into the voltage excitation/input matrix Vmesh.

For (ii), can we treat the dependent source as a normal element like a resistor in the derivation of the impedance matrix?

The matrix equation of the circuit network is characterized by

Vmesh = Z * I

where Vmesh = voltage excitation matrix

Z = impedance matrix

I = mesh current matrix

Example circuit problem shown in attachment:

Thansk for help!

Power is not energy. Power is measured is in watts and energy in watt-seconds (or joules' date=' BTUs, Kwhs etc.)

 

If you burn a certain amount of fossil fuel, you will get a certain amount of Energy which equates to supplying a certain number of watts for a certain amount of time. Supplying 50 watts for 1 sec is the same as supplying 1 watt for 50 secs.

 

So let's assume that you use the 50 joules of energy gained from burning your fossil fuel to "spin up" a generator. Ignoring friction, the generator will continue to turn until a load is placed on it. You hook up your 10 ohm light bulb. The resistance of the light bulb determines the current, so:

 

[math']I= \frac{250kv}{10 \Omega}= 25ka [/math]

 

[math]P = 250kv(25ka)= 6.25 gw[/math]

 

50 joules = 50 watt-seconds so

 

[math]t= \frac{50w-ses}{6.25gw} = 0.000000008 sec. [/math]

 

meaning that the bulb will glow for 0.000000008sec before using up the energy stored in the spun up generator.

 

On the other hand:

If you burn the fossil fuel at such a rate such to allow the generator to supply a constant 50 watts, then it doesn't matter how much wattage the bulb could use, it is only supplied with 50 watts. The amperage will drop off to the point where the wattage used by the bulb equals that supplied by the generator. (As the bulb demands more current, this current causes a counter force in the generator which opposes its rotation. The fossil fuel has to supply the energy to overcome this opposition. A balance is met where the current supplied matches the rate at which the fuel is burned.) While the load determines how much currents it demands, the source determines how much current can be supplied. And if the former exceeds the later, you get the later.

 

It is for this same reason that you cannot simply string 8 AAA batteries in series to jump start a car. The AAA's have sufficient voltage (12v) but they cannot supply the needed current.

I have realized the limitation of current in embedded system design of a particular application. The design is logically correct in terms of flow diagrams, but because, it drives plenty of LEDs, including the 7-segment display and a pair of dc motors, if the choice of batteries is not correct, even though the voltage input is right, the system will not work!

True, in the way as YT2095 has described, you can generate electricity, but the current generated in the coil (I think in pico to microAmpere range) is too small for any use in most electrical applications. Even the least power-hungry device like the LED, I doubt it will light up.

Here are two questions I am concerning.

2.This question is relevant to my thought.

How is the current in the secondary coil determined?

by V=IR?

I think it is by P=IV.

By then' date=' how could any appliance in the secondary coil affect the current?

Consider a step-up transformer.

If the V in 2nd coil is very large, V^2/R will violate the law of conservation of energy.[/quote']

 

The above analysis is wrong.

During the step-up process, extra "resistance" is created in the secondary coil due to impedance tranformation from the primary coil to secondary coil which is dependent on the turns ratio.

So in effect, Power = VI in the primary coil = VI in the secondary coil.

 

Correct me if I am wrong! Thanks

Hi,

I know how to bias a BJT transistor to operate in the active region, so that the amplifier circuit can operate as a small-signal amplifier. Two methods

(i) Use biasing resistors to form a self-biasing circuit.

(ii) Use diode biasing, coupled with biasing resistors.

Qn1

However, how do we bias the transistor circuit to act as small signal amplifier, if MOSFETs are used instead?

Design of dc biasing circuit for MOSFET as an amplifier???

I read from my textbook that we need to bias the MOSFET in the saturation region, which is quite different from the BJT amplifier dc biasing design.

The relation of MOSFET in saturation region is

Id = K(Vgs - Vt)^2

where Id = dc drain current

K = a property of MOSFET (What exactly is this?)

Vgs = dc gate-source voltage

Vt = threshold voltage of MOSFET

Qn2

Is there any difference in dc biasing design of n-type enhancement MOSFETs with n-type depletion type MOSFETs? What is the difference?

Qn3

After the MOSFET biasing point is fixed (saturated), we input an small ac signal in the input port, to get an amplified output signal in the output port, with the midband gain depending on the amplifier design.

How is the small signal equivalent circuit model different for enhancement and depletion type MOSFETs?

My answer is, they are essentially the same, but with one slight difference:

vgs for enhancement type is positive, while vgs for depletion type is negative, am I correct?

Qn4

In the small signal model of MOSFET, the ac drain current

id = transconductance * vgs ---Linear, voltage-controlled current source

Why is it this formula, and NOT Id = K(Vgs - Vt)^2?

transconductance = 2K(Vgs - Vt) --Enhancement and Depletion type MOSFET

Yes i agree.

Start learning from the basics, the simplest, which is the Intel 8086/8088 microprocessor rich instruction set, aseembly directives, software architecture of the 8086/8088 and hardware interfacing of the RAM, ROM, timer chip, UART chip, and plenty of others.

This is because, Intel's microprocesor chip is upward-compatible, so even if you write a assembly code for 8086/8088, you can run and implement it on let's say 80486 or higher processor, your Pentium 4.

Hi,

I am now doing a project to write a 16-bit DOS piano program to play the 12 notes in an octave, which I have completed. But this program must also be able to "talk" to another computer through null modem R2-232 connection so that the note played on the local PC is also played on the terminal PC.

I have a severe problem accessing the COM1 port on the Window XP platform, due to protected rights of accessing the I/O ports in Windows NT and higher operating systems, even when I am using the 16-bit DOS emulator program NTVDM.exe. Is there any quick solution to this problem, how am I going to bypass the Privilege level access of I/O ports (COM1 port) with my written software program? (For example, adding a few assembly codes? How?)

Thanks

how does a booster pack work?

 

^repliacte one.

 

also you could extend the aerial.

Most wi-fi systems that you bought from the store cannot extend tha aerial antenna, it is fixed. The only thing we consumers could do to increse signal strength and coverage is to position the antenna of the wireless accesspoint 90 degrees up!

i dont think u CAN charge a capacitor to the max. i think it involves

 

1-e^(-t)

I have worked out the voltage-time relationship of the capacitor-resistor network using 1st principles.

The solution is attached in the word document I have uploaded.

V = v0 - v0*exp(-t/RC) for charging case.

Cheers!

The general solution of the de.doc

Any strong reason why you use NaOH as the electrolyte, instead of CuSO4 solution or other metallic solution???

Err, without moving the position of the router and the computer???

If it is at the end of the reachable radius, the only thing that you can do is to remove as much physical obstruction between the line of sight of the router and the computer. Anything metallic will block EM waves and reduce the signal strength. Also you can try locating your wireless router higher up so as to reduce any possible physical obbstruction.

Another way you may try is to move a little bit of the wireless card postition to move out of any possible multipath fading phenomenon.

But these two methods may not be that effective after all. The most ffective solution is only to move the computer nearer to the wireless router.

Cheers,

Yeok Peng

What program did you use to draw that pretty diagram, Jakari?

Are you assuming that the other radio is in fact already turn on?

Anyway, based on what I know, it should not affect the intensity of the other radio much, even though the radio you are turning on is activated through remote control. The radio frequency that the remote control is using a frequency band that is quite far away from the spectrum of the actual radio signals from the radio station.

Very Very simple radio!

An antenna

A few variable capacitors

inductor coils

resistors

Make a RLC resonant circuit using these and we can tune in to the frequency you want by varying the capacitance of the variable capacitor.

It works but it is a very poor quality one.

In modelling dieelectric breakdown using the percolation path effective resistance model, Why can we use ohm's law to model the resistance of the percolation path and even the resistance of the inverting channel formed under the dielectric?

Another question, in localized heating effect, it will cause dopant redistribution. What is the exact mechanism for activating these dopant atoms?

In such nano-size transistor as in MOSFETs, how probable is the dielectric going to break down at normal operating electric field or stressing voltage?

There are many factors that will aid dielectric breakdown in the metal oxide layer, example localized high temperature, dieletric crystal defects, dielectric strength, applied gate voltage, size of the transistor(thereby size of the oxide layer), etc.

But my question is that since many factors cause DB, how does manufacturers of MOSFETs ensure that lower percentage of faultly transistors is produced in the market? The moment DB occurs in any transistor in a processor chip for example, and mind you a Pentium 4 processor consists billions of transistors, the I-V characteristics of that DB transistor degrades into ohmic and not transistor-like anymore. This will affect the overall performance and quality of the whole processor chip as a whole.

Maybe your question has been stated wrongly.

As YT2095 siad, the final charge left on each capacitor will be zero after you leave the circuit for at least a few time constants (After the transient effects have dissipated).

This is because all the charge will have been dissipated by through the short-circuit link.

Sorry, I didn't see your cars. Do most of you see it???

Assume that the cars are travelling towards each other at your stated speed, both speed are stated measured with respect to the Earth.

The Gamma factor for SP is sqrt(1-v^2/c^2) is so close to unity that the effects of SP is very unobservable.

Even if you add up the velocity according to Lorentz addition of velocity

= (v(ba)-v(ca))/(1-v(ba)v(ca)/c^2), the addition is very close to the answer by adding v(ba) and -v(ca), due to the speed involved not at least 0.2 times the speed of light.

At such low speeds, the effect of special relativity cannot be observed!

Though I am still studying electrical engineering, I still have not learnt how engineers go about lining up all the minute components of the chip in nano-scale? Anyone can enlighten me on that?

Anyway, in nano-scale, there are many contacts made, such as metallic-semiconductor contacts, semiconductor-dielectric contacts etc. Sometimes, I wonder since they are fabricated in nanoscale, how come the minute distance between them do not cause dielectric breakdown, and causes streaks of discharge across the chips?

From what I know from Einstein's GR, there is no speed in gravity. Gravitational force is one of the hardest forces for scientists to try to unify under a single unified theory, just as electic field and magnetic field can be classified under electromagnetism. Its nature is due to the distribution of mass in the space-time fabric, and the effect of gravitational force is instantaneous.

Gravitational force are not physical objects or particles. So the ultimate speed c does not apply here.

I wonder how they calculate the temperature of cosmic background, after measuring it using radio receivers?

From what I've read, one of the possible application of this thread discussion is to create a third party planet like ring for people to live on, if technology allows.

If a large ring can be made to rotate at very high constant speed v in a circle, we know that an acceleration mv^2/r = mrw^2 is being directed towards the centre of the ring. Using the gravity-acceleration equivalence principle, this will produce a force in the other direction away from the centre of the circle. This may be confusing to some, so I use an analogy. If you are in a lift and the lift starts accelerating upwards from rest, you will feel heavier, just as if extra weight has been added and this extra weight is also directing downwards opposite to the direction of accleration of the lift. So simliarly, the force created by the accelerated frame will be opposite in direction to the acceleration.

If people are to live on this large ring, they will feel their own weight pulling them downwards away from the centre of the ring, and all will agree that their sky (upward) will be the centre of the large ring. They will not notice themselves rotating in a circle if the diameter of the ring is made large enough. What they will experience is like the same experience back on earth.

In Einstein's general relativity,

the effects of acceleration and the gravity is the same.

Imagine that you are in a spaceship in space very far away from any star or planets moving with constant acceleration in a straight line equal to 9.81 m/s^2 = g, you will feel yourself being pulled to the floor of the ship, as if you can feel your weight similar to what you experience back on earth.

From the understanding of Newtonian mechanics, you know that acceleration can also be due to a change of direction, and you will experience a centripetal acceleration towards the centre of the circular path as you move in a circle. Hence rotation of an object can effectively produce the same effect of gravity due to the Einstein's equivalence of gravity and acceleration. In other words, the effects of accelerated frame and gravitational force due to presence of mass are indistinguishable, both will deform the space-time fabric in the vicinity.