Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
LP PROBLEM SET 2
OR FORMULATION PROBLEMS
These problems are adapted from the following text books and are for classroom discussion only.
1.
2.
3
4.
'Quantitative Methods for Business Decisions', Gallagher and Watson.
'Quantitative Approaches to Management
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
Lecture  26 Equalizer, Eye Pattern 10032007
1
2
Intersymbol Interference (ISI)
3
Zero forcing equalizer: cks are the tap gains. The time delay is chosen to be the symbol interval Tb. pO(t) must satisfy the Nyquist criteria.
4
Received Pulse
After Equa
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
Lecture  25 Line Codes. 8032007
1
Power Spectral Density of NRZ Line Code
2
PSD of RZ and Manchester NRZ Codes
3
Intersymbol Interference (ISI)
4
Raised Cosine Filter
5
Response for different rolloff factors.
6
Response for different rolloff factors
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
Lecture  23 DPCM , DM & Line Codes. 1032007
1
Delta Modulation
2
D Modulator
3
Two versions of D Modulator
4
Line Codes PCM Signaling Formats
Unipolar Signaling: A binary 1 is represented by high level ( +5 Volts or A Volts) and a binary 0 by zero lev
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
Lecture  22 Quantization 27022007
1
2
PCM Generation
3
Problem with Uniform Quantization
SNR is an indication of the quality of the received signal SNR is directly proportional to signal power and varies from talker to talker by as much as 40 dB. The
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
The Noise objective was 3pW/km. The total noise power measured at the end of 6400 km was 8000 pW, which is less than 3pW/km. The (S/ N)O was 40 dB. 2 coaxial tubes required for 10,800 channels, one for Go and the other for Return. For L5  22 tubes are th
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
Lecture 8
Frequency Modulation FM Generation
FM Generation
1.Direct Method 2.Indirect Method (Armstrong Method)
Narrowband FM Generation (NBFM) Wideband FM Generation Combination of NBFM and Frequency multipliers
Narrow Band FM:
x (t) = Ac cos[ct + (t)] F
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
Types of AM :
1.Ordinary AM Carrier and both sidebands. 2. DSBSC Double Sideband Suppressed Carrier. 3. SSBSC Single sideband suppressed Carrier. 4. VSB Vestigial Sideband. VSB is a compromise between DSB & SSB.
VSB Signal :
VSB modulation is used for t
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
Fourier transform of an Impulse train
An impulse train in time domain is transformed into another impulse train in the frequency domain.
Sampling Theorem(contd.)
Impulse train and
its spectrum
Rayleighs Energy Theorem:
x(t)x*(t)dt = X ( ) X *( )d Sxx( )
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
QUANTITATIVE METHODS II
MATERIAL FOR CLASS DISCUSSIONS
& PROBLEM SETS  PACKET 2
Sections A & B
1
PRODUCT MIX AT MANVI MOTORS
Manvi Motors of Malaysia produces cars under an agreement with Suzuki of Japan and
trucks under an agreement with General Motors
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
1
GOAL PROGRAMMING
Nicolo Investments
Nicolo Investment Advisors is facing the following problem. A client has up to $80,000 to
invest and, as an initial investment strategy, would like the portfolio restricted to a mix of the
following two stocks:
Stock
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
Harvard Business School
9183133
Rev. 11/83
Gartland Steel
Thursday, October 11, 1979. Dan Crossan, Director of Environmental Engineering at Gartland Steel,
returned from lunch and found a memo left for him by Jay Peeler, Senior Project Engineer. Crossan
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
1
INTEGER PROGRAMMING
Advertisement Decisions
The Big Bucks Placements Company wants to make a decision on which advertising
media to use. Its target is to reach 20,000 people at minimum advertising cost. The media
through which it may advertise are three
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
NONLINEAR PROGRAMMING
VIJAYANAGARA COMMUNICATIONS
Vijayanagara Communications currently provide cellular phone service in Bangalore.
They wish to expand their operations to provide intercity service between four cities in
south Karnataka. They are, Banga
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
Lecture 40 Spread Spectrum 21042007
1
Spread Spectrum Communication Systems
2
Spreading in the presence of White Noise.
3
Types of Jamming
4
Spectrum before and after Jammimg
5
Low Probability of Intercept (LPI) & SSMA
6
Spread Spectrum Techniques
7
Aut
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
Lecture 39 Analog Comm. System Noise Performance Comparison, Bandwidth Efficiency etc. 19042007
1
Comparison of Noise Performance of Analog Systems
2
Bandwidth Efficiency Diagram
3
Comparison of Mary PSK with Ideal System
4
Bandwidth Efficiency Plane f
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
Lecture2
Review of Signals and Systems
Classification of signals: 1. Deterministic or Random (Stochastic ) Also Classified as Discretetime(digital) Continuous time(analog) Further Classified as 1. Periodic 2. Aperiodic Also classified as Energy signal 0
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
Some problems illustrating the principles of duality
I n this le cturewelook at som proble s that use e m s t he re sults from Duality the (as discusse in ory d C hapte 7). r
Problem 7. Problem Set 4.2D Page 130 Consider the LPP Maximize z = 5 x1 + 2 x2 +
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
Dual simplex met hod for solving t he pr imal
I n thi s l ectur e we descr i be the i mpor tant Dual Si mpl ex method and i l l ustr ate the method by doi ng one or t wo pr obl ems.
Dual Simplex Method
Suppose a basic solution satisfies the optimality con
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
D ualit y t heor ems Finding t he dual opt imal solut ion fr om t he pr imal opt imal t ableau
Dual problem in Matrix form In this lecture we shall present the primal and dual problems in matrix form and prove certain results on the feasible and optimal s
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
Dual Problem of an LPP Given a LPP (called the primal problem), we shall associate another LPP called the dual problem of the original (primal) problem. We shall see that the Optimal values of the primal and dual are the same provided both have finite fea
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
Deterministic Dynamic Programming
Dynamic Programming (DP) determines the
optimum solution to an nvariable problem by
decomposing it into n stages with each stage
constituting a singlevariable sub problem.
Recursive Nature of Computations in DP
Computat
Birla Institute of Technology & Science, Pilani  Hyderabad
OPtimization
MATHEMATIC AAOC C222

Fall 2007
The Assignment Model " The best person for job" is an apt description of the assignment model. The general assignment model with n workers and n jobs is presented below: Jobs 1 2 . n 1 c11 c12 c1n Workers 2 c21 c22 c2n n cn1 cn2 cnn
The element cij is the