TOPIC – LINEAR PROGRAMMING Linear Programming is a mathematical procedure for determining optimal allocation of scarce resources. Requirements of Linear Programming • all problems seek to maximize or minimize some quantity • The presence of restrictions or constraints • There must be alternative courses of action • The objective and constraints in linear programming must be expressed in terms of linear equations or inequalities Objective
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An Introduction to Linear Programming Steven J. Miller∗ March 31‚ 2007 Mathematics Department Brown University 151 Thayer Street Providence‚ RI 02912 Abstract We describe Linear Programming‚ an important generalization of Linear Algebra. Linear Programming is used to successfully model numerous real world situations‚ ranging from scheduling airline routes to shipping oil from refineries to cities to finding inexpensive diets capable of meeting the minimum daily requirements. In many of these problems
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Announcements and Demos (0:00-10:00) • This is CS50. • Check out what is possible in the programming language called Scratch that we will begin the course with! Scratch will enable you to wrap your mind around the fundamental constructs of programming while making a cool game or animation. • Be sure to check out the second annual CS50 Puzzle Day this Saturday! Thanks to Facebook for sponsoring! • CS50 is all about getting you through CS50. We want you to make it to the final days and gain that
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Sum=i+ odd; Hanly‚ Chapter 8‚ Programming (pp. 396-397)‚ number 1 1. #include<stdio.h> Int main <void> Int list{11}; Int n‚ I‚ sum; Double %_of_total; { Printf(“please enter values\n”) Scanf(“%d”‚&n) For(i=0‚i<=n‚++i) Sum=n/10; %_of_total = sum; Printf(“The%d is the %_of_total %d\n”‚ n‚ %_of_total); Return (0); } Hanly‚ Chapter 8‚ Self-Check Exercises (p. 410)‚ numbers 3-4 3.return (int‚ 1= I <=in_use‚ 0= I =in_use); 4.for(i=0‚ i<=data‚ ++i) Hanly‚ Chapter 8‚ Programming (p. 410)‚ numbers 1‚ 3 1. Int
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Procedural programming It is technique that problem solving in “divide and conquer” method. It means program reach the complex problem step by step and break it into separate subclasses. So‚ it is easy to solve the problem. Each sub classes have the connection with others. So this type of style can be active when it comes to the complex solutions. For example‚ if you want to calculate the month-end closing balance for a bank account‚ then the required steps would be as follows. First‚ you acquire
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Research 153 (2004) 117–135 www.elsevier.com/locate/dsw An integer programming formulation for a case study in university timetabling S. Daskalaki b a‚* ‚ T. Birbas b‚ E. Housos b a Department of Engineering Sciences‚ University of Patras‚ GR-26500 Rio Patras‚ Greece Department of Electrical and Computer Engineering‚ University of Patras‚ GR-26500 Rio Patras‚ Greece Abstract A novel 0–1 integer programming formulation of the university timetabling problem is presented. The model
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Procedural Programming vs Object Oriented Programming When writing code for a program it is very important to make sure that you use the best language for what the client needs. Prior to making a decision on what language to use‚ a programmer needs to decide which method he or she wants to use. The two most common methods used by coders in the field today are procedural and object oriented programming (OOP). Making the decision to use an incorrect option could run cause problems during the maintenance
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8 6.2 Arrays (Cont.) • Index – Also called subscript – Position number in square brackets – Must be positive integer or integer expression – First element has index zero a = 5; b = 6; c[ a + b ] += 2; • Adds 2 to c[ 11 ] 9 Common Programming Error 6.1 Using a value of type long as an array index results in a compilation error. An index must be an int value or a value
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Object-oriented Programming/Event-Driven Programming versus Procedural Programming Professor Computer Program Design Object-oriented Programming/Event-Driven Programming versus Procedural Programming There are many advantages of using Object-oriented Programming (OOP) over Procedural Programming (PP). When using inheritance‚ you can develop new classes more quickly by extending existing classes that already work; you need to concentrate only on new features added by the new class.
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Z00_REND1011_11_SE_MOD7 PP2.QXD 2/21/11 12:39 PM Page 1 7 MODULE Linear Programming: The Simplex Method LEARNING OBJECTIVES After completing this chapter‚ students will be able to: 1. Convert LP constraints to equalities with slack‚ surplus‚ and artificial variables. 2. Set up and solve LP problems with simplex tableaus. 3. Interpret the meaning of every number in a simplex tableau. 4. Recognize special cases such as infeasibility‚ unboundedness and degeneracy. 5
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