The homework problems for Module 4 are: 2-24, 34, 36, 38 (you only have to do part A for these problems. You do not have to do the part B graphical solutions) and 3-10, 12 (parts B and C for Problem 12), 28, 30. Please use Excel solver function.

I posted an annotated solution to Problem 2-5. This problem is an examplar for both the chapter 2 and 3 problems. In this example I show how I typically set up a problem. First I set up the linear programming model and then develop a parallel set-up to use as input to the Solver add-in. I use this strategy because I first like to set up the problem solution before I worry about setting up the parameters for using Solver. 24. Universal Claims Processors processes insurance claims for large national insurance companies. Most claim processing is done by a large pool of computer operators, some of whom are perma-nent and some of whom are temporary. A permanent operator can process 16 claims per day, whereas a temporary operator can process 12 per day, and on average the company processes at least 450 claims each day. The company has 40 computer workstations. A permanent operator generates about 0.5 claim with errors each day, whereas a temporary operator averages about 1.4 defective claims per day. The company wants to limit claims with errors to 25 per day. A per-manent operator is paid $ 64 per day, and a temporary operator is paid $ 42 per day. The company wants to determine the number of permanent and temporary operators to hire in order to mini-mize costs. a. Formulate a linear programming model for this problem.

34. Gillian’s Restaurant has an ice- cream counter where it sells two main products, ice cream and frozen yogurt, each in a variety of flavors. The restaurant makes one order for ice cream and yogurt each week, and the store has enough freezer space for 115 gallons total of both products. A gallon of frozen yogurt costs $ 0.75 and a gallon of ice cream costs $ 0.93, and the restaurant budgets $ 90...

...RESEARCH PAPER ON
LINEARPROGRAMMING
Vikas Vasam
ID: 100-11-5919
Faculty: Prof. Dr Goran Trajkovski
CMP 561: Algorithm Analysis
VIRGINIA INTERNATIONAL UNIVERSITY
Introduction:
One of the section of mathematical programming is linearprogramming.
Methods and linearprogrammingmodels are widely used in the optimization of processes in all sectors of the economy: the development of the production program of the company, its distribution on the performers, when placing orders between the performers and the time intervals, to determine the best range of products, in problems of perspective, current and operational planning and management, traffic planning, defining a plan of trade and distribution, in the problems of development and distribution of productive forces, bases and depots of material handling systems, resources, etc. especially widely used methods and linearprogrammingmodel for solving problems are savings (choice of resource-saving technologies, preparation of mixes, nesting materials), production, transportation and other tasks.
Beginning of linearprogramming was initiated in 1939 by the Soviet mathematician and economist Kantorovich in his paper "Mathematical methods of organizing and planning...

...Q.1. What is a linearprogramming problem ? Discuss the steps and role of linearprogramming is solving management problems. Discuss and describe the role of liner programming in managerial decision-making bringing out limitations, if any.
Ans : LinearProgramming is a mathematical technique useful for allocation of scarce or limited resources to several competing activities on the basis of given criterion of optimality.
The usefulness of linearprogramming as a tool for optimal decision-making on resource allocation, is based on its applicability to many diversified decision problems. The effective use and application requires, as on its applicability to many diversified decision problems. The effective use and application requires, as a first step, the mathematical formulation of an LP model, when the problem is presented in words. Steps of linearprogrammingmodel formulation are summarized as follows :
STEP 1 : Identify the Decision Variables
a) Express each constraint in words. For this you should first see whether the constraint is of the form >/ (at least as large as), of the form \< (no larger than) or of the form = (exactly equal to)
b) You should then verbally express the objective function
c) Steps (a) and (b) should then allow you to verbally identify...

...TOPIC – LINEARPROGRAMMINGLinearProgramming is a mathematical procedure for determining optimal allocation of scarce resources.
Requirements of LinearProgramming
• 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 inlinearprogramming must be expressed in terms of linear equations or
inequalities
Objective Function it maps and translates the input domain (the feasible region) into output range, with
the two-end values called the maximum and minimum values
Restriction Constraints it limits the degree to which we can pursue our objective
Decision Variables represents choices available to the decision maker in terms of amount of either inputs or outputs
Parameters these are the fixed values in which the model is solved
Basic Assumption of LinearProgramming
1. Certainty- figures or number in the objective and constraints are known with certainty and do not vary
1. Proportionality - for example 1:2 is equivalent to 5:10
1. Additivity - the total of all the activities equals the sum of the...

...LINEARPROGRAMMING
INTRODUCTION:
The term ‛programming′ means planning and it refers to a particular plan of action amongst several alternatives for maximizing profit or minimizing cost etc. Programming problems deal with determining optimal allocation of limited resources to meet the given objectives, such as cost, maximum profit, highest margin or least time, when resources have alternative uses.
The term ‛linear’ means that all inequations or equations used and the function to be maximized or minimized are linear. That is why linearprogramming deals with that class of problems for which all relations among the variables involved are linear.
Formally, linearprogramming deals with the optimization (maximization or minimization) of a linear function of a number of variables subject to a ¹equations in variables involved.
The general form of a linearprogramming problem is
Optimize (Maximize or Minimize) Z = c1x1 + c2x2 + ……..+ cnxn
Subject to
a11 x1 + a12x2 + ….. + a1n xn (≤ , = , ≥) b1
a21 x1+ a22x2+ ….. + a2nxn (≤ , = , ≥ ) b2
. . . .
am1 x1+ am2 x2 +...

...
QUANTITAVE TECHNIQUES OF BUSINESS
ASSIGNMENT NO;
5
SUBMITTED TO;
PROF. ADNAN
SUBMITTED BY;
NIDA WASIF
ROLL # 54
MC-B
TOPIC;
LINEARPROGRAMMING
DATE;
5 JUNE, 14
UNIVERSITY OF CENTRAL PUNJAB
INTRODUCTION TO LINEARPROGRAMMINGLinearprogramming (LP; also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linearprogramming is a special case of mathematical programming.
It is a mathematical technique used in computer modeling to find the best possible solution in allocating limited resources (energy, materials, machines, money etc) to achieve maximum profit or minimum cost.
LinearProgramming is a method of expressing and optimizing a business problem with a mathematical model. It is one of the most powerful and widespread...

...
LinearProgramming
After completing this chapter you should be able to:
identify a product which maximises the contribution per unit of scarce resource when there is only one scarce resource, and determine the optimum solution.
formulate an LP model to solve for the optimal product mix which maximises profits, or for cost minimisation problems to minimise costs.
solve 2 variable problems graphically.
use a spreadsheet to solve LP problems with any number of variables.
interpret the sensitivity reports of spreadsheet solutions to LP problems to test objective function coefficient sensitivity, determine shadow prices and RHS ranging.
perform throughput accounting and solve problems using the concept of the Theory of Constraints.
Introduction
In this chapter we continue with our profit planning, or product mix, decisions. We extend CVP analysis in the last chapter by introducing the notion of scarce resources. Although CVP analysis does not provide answers regarding optimum product mixes (mixes which maximise profits or minimise costs) one advantage of CVP analysis is that it focuses attention on products with high contribution margins. Managers and salespeople can often direct their efforts to increasing output and sales of high contribution margin products and thereby maximise the contribution towards fixed costs and profits. Unfortunately, it is not always desirable to attempt to maximise the sales of high...

...The development of linearprogramming has been ranked among the most important scientific advances of the mid 20th century. Its impact since the 1950’s has been extraordinary. Today it is a standard tool used by some companies (around 56%) of even moderate size. Linearprogramming uses a mathematical model to describe the problem of concern. Linearprogramming involves the planning of activities to obtain an optimal result, i.e., a result that reaches the specified goal best (according to the mathematical model) among all feasible alternatives.
LinearProgramming as seen by various reports by many companies has saved them thousands to even millions of dollars. Since this is true why isn’t everyone using LinearProgramming? Maybe the reason is because there has never been an in-depth experiment focusing on certain companies that do or do not use linearprogramming. My main argument is that linearprogramming is one of the most optimal ways of resource allocation and making the most money for any company today.
I used (in conjunction with another field supporter – My Dad) the survey method to ask 28 companies that were in Delaware, New Jersey, and Pennsylvania whether they were linearprogramming users. In addition, I...

...Online Tutorial
The Simplex Method
of LinearProgramming
Tutorial Outline
CONVERTING THE CONSTRAINTS TO
EQUATIONS
SOLVING MINIMIZATION PROBLEMS
SETTING UP THE FIRST SIMPLEX TABLEAU
KEY TERMS
SIMPLEX SOLUTION PROCEDURES
SOLVED PROBLEM
SUMMARY OF SIMPLEX STEPS FOR
MAXIMIZATION PROBLEMS
DISCUSSION QUESTIONS
ARTIFICIAL AND SURPLUS VARIABLES
SUMMARY
PROBLEMS
3
T 3-2 O N L I N E T U T O R I A L 3
THE SIMPLEX METHOD
OF
L I N E A R P RO G R A M M I N G
Most real-world linearprogramming problems have more than two variables and thus are too complex for graphical solution. A procedure called the simplex method may be used to find the optimal
solution to multivariable problems. The simplex method is actually an algorithm (or a set of instructions) with which we examine corner points in a methodical fashion until we arrive at the best solution—highest profit or lowest cost. Computer programs and spreadsheets are available to handle the
simplex calculations for you. But you need to know what is involved behind the scenes in order to
best understand their valuable outputs.
CONVERTING THE CONSTRAINTS TO EQUATIONS
The first step of the simplex method requires that we convert each inequality constraint in an LP formulation into an equation. Less-than-or-equal-to constraints (≤) can be converted to equations by
adding slack variables, which represent the...