Chapter 7: Linear Programming. 7.2: LINEAR PROGRAMMING
Abstarct: We will learn to state the nature of
a linear programming problem along with the introduction of terminology associated with it, and then developing a method for its solution geometrically
Qualitative Choice Analysis Workshop
7.2 Linear Programming Dr. Raja Mohammad Latif Objective: To state the nature of a linear programming problem, to introduce terminology associated with it, and to solve it geometrically.
Dr. Raja Latif. 8.3 Annuity Due
Annuity Due: Annuities that have payments at the beginning of the interest period are called annuities due.
The future value of an annuity due of n payments of R dollars each at the beginning of consecutive interest perio
1 A Standard Maximum Problem is a linear program in which we wish to maximize the objective function F = c1x1 + c2x2 + . . . + cnxn subject to constraints of the form a 11 x 1 + a 12 x 2 + . . . + a 1n x n b 1 a 21 x 1 + a 22 x 2 + . . . + a 2n x n b 2 .
Math131043 7.3Linear Programming.1 7.3 Linear Programming 211Tan10* Minimize C 2x 5y 211Tan11*Minimize C 6x 3y subject to the constraints: 4x 2x x x 0 y y , 40 30 y 0
Solution. 4x y 40, 2x y 30, x 3y 30
30 y 20
Qualitative Choice Analysis Workshop
7.1 Linear Inequalities in Two Variables Dr. Raja Mohammad Latif We will geometrically represent the solution of a linear inequality in two variables and will extend this representation to a s
Dr. Raja Latif. Math 131(043)8.1, Pg:1
Chapter 8: Introduction to Probability and Statistics
8.1: Basic Counting Principle and Permutations Basic Counting Principle: . n1. n2. . . . nk.
Permutation: An ordered arrangement of r objects, without repetition,
Dr. Raja Latif. Math 131 (043) Sec: 8.2. Pg:1 Chapter 8: Introduction to Probability and Statistics 8.2: Combinations and Other Counting Principles
Combinations of n Objects: To derive a formula for determing the number of combinations of n objects taken
Dr. Raja Latif. Math 131 (043) Sec8.3 Pg:1
8.3: Sample Spaces and Events
EXPERIMENT An experiment is an activity with observable results. SAMPLE POINT : an outcome of an experiment. SAMPLE SPACE : the set consisting of all possible sample points of an exp
Dr. Latif. Math 131(043)8.4: Probability. Pg:1 Ch:8: Probability. 8.4: Probability 1.402TAN24. A pair of fair dice is cost. What is the probability that: a. The sum of the numbers shown uppermost is less than 5? b. At least one 6 is cast? a. The required
8.6: Independent Events
437TAN17. A pair of fair dice is cast. Let E denote the event that the number landing uppermost on the first die is 3 and let F denote the event that the sum of the numbers landing uppermost
8.5: Conditional Probability
Formula for Conditional Probability: If E and F are events associated with an equiprobable sample space and F , then PE|F
It is shown that PE c |F 1 - PE|F. Definition: The condi
MATH 131 (062) Finite Mathematics. Chapter 8: Probability. June 3, 2007.
Dr. Raja Latif and Mohammad latif and Abdul Latif and Dr. Raja Mohammad Abdul Latif
Contents 8.1-2:Basic Counting Principle and Permutations;Combinations and Other Counting Principle
Chapter 6: MATRIX ALGEBRA Dr. Raja Mohammad Latif We will show how to reduce a matrix and to use matrix reduction to solve a linear system.
Math 131-052. Dr. Raja Latif 6.4-6.5: Method of Reduction Performing any one of the following Row Operations on the
Dr. Raja Latif.Math 131 Summer 2005. Pg:1
Ch 5 Finance Mathematics
5.1: COMPOUND INTEREST Compound Interest Formula: For an original principal of
P, the formula S P1 r n gives the compound amount S at the end of n interest (or conversion) periods at the p
Dr. Raja Latif. Math 131.5.3 ANNUITIES
Objective: To introduce the notions of ordinary annuities and annuities due. To use geometric series to model the present value and future value of an annuity. Geometric Sequence: If a and r are nonzero real number
Dr. Raja Latif. Math 131 (051) Chapter 1.1.Applications of Equations Pg:1
1.1 APPLICATIONS OF EQUATIONS
Slvd. Examples Home Work 1, 2, 3, 4, 7 12, 16, 28, 33 Rcmd. Problems 1, 11, 13, 21, 25, 33, 35, 37 Algebraic methods are very useful in solving applied
Dr. Raja Latif. Dept. Of Mathematics Chapter 3: Lines, Parabolas, and Systems
3.1: Lines We develop the notion of slope and different forms of equations of lines. Slope of a Line Many relationships between quantities can be represented conveniontly by
3.5: NonLinear Systems Dr. Raja Mohammad Latif
Math 131-052. Dr. Raja Latif
1 3.5 Nonlinear Systems
=Lecture Sec 3.5 Begins now= The method of substitution is often useful when we have a system of equations in which one equation is linear and the other
Chapter 3: Lines, Parabolas and Systems 3.2: APPLICATIONS AND LINEAR FUNCTIONS DR. RAJA LATIF
September 17, 2005
We develop the notion of demand and supply curves and introduce linear functions.
SUPPLY AND DEMAND: The curves that show the quantit
Chapter 3: Lines, Parabolas, and Systems 3.4: Systems of Linear Equations Dr. Raja Mohammad Latif
Department of Mathematical Sciences, KFUPM
1 3.4: Systems of Linear Equations
=Lecture Sec 3.4 Begins now= Home Work: 26; 28; 29; 34; 37; 39; 41 Independen
3.6 Applications of Systems of Equations Dr. Raja Mohammad Latif OBJECTIVE: To solve systems describing equilibrium and break-even points.
Dr. Raja Latif. Math 131 - 052 (Feb. 12 - June 10, 2006)
1 3.6 Applications of Systems of Equations
=Lecture Sec 3
Dr. Raja Latif. 3.2: Applications and Linear Functions. Math 131(043) Pg: 1
SUPPLY AND DEMAND: The curves that show the quantity that will be supplied at a given price and the quantity that will be demanded at a given price are called SUPPLY and DEMAND CU
Dr. Raja Latif. Finite Mathematics.Pg:1 Dr. Raja Latif. 5.3 ANNUITIES Objective: To introduce the notions of ordinary
annuities and annuities due. To use geometric series to model the present value and future value of an annuity. Geometric Sequence: If a
Math 131 Finite Mathematics. Dr. Raja Latif
Chapter 5 Mathematics of Finance In this chapter we discuss mathematical methods and formulas that are useful in business and personal .nance.
5.1 COMPOUND INTEREST OBJECTIVE: To extend the notion of compound in
Dr. Raja Latif.Finite Mathematics.Pg:1 Math131(043Smr2005)Finite Mathematics. 10.3 Interest Compounded Continuously Objective: To extend the notion of compound interest discussed in Chapter 8 to the situation where interest is compounded continuously. To
Chapter 1: Applications of Equations and Inequalities Dr. Raja Mohammad Latif In this chapter, we will apply equations to various life situations. We will do the same with inequalities, which are statements that one quantity is greater than, less than, no