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# 6417c02 - INTRODUCTION TO LINEAR PROGRAMMING CONTENTS...

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1 INTRODUCTION TO LINEAR PROGRAMMING CONTENTS Introduction to Linear Programming (Chapter 1) Applications of Linear Programming

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2 Resource Allocation Problem A manufacturing facility makes a number of products 1, 2, 3, . ., n. There are m different types of raw materials used to make these items, 1, 2, . . , m. The cost of unit value of i th raw material is r i and we have b i units of raw material available. Producing one unit of product j requires a ij units of raw material i. Each unit of product j can be sold at the price of s j . Decide the production quantities of different products to maximize the profit.
3 Resource Allocation Problem (contd.) Decision Variables : x j = number of units of product j Objective Function : Maximize the total profit Profit per unit of product i: c j = s j - i=1,n r i a ij Total profit: j=1,n c j x j Maximize j=1,n c j x j Resource Constraints : We do not exceed the availability of any raw material. j=1,n a ij x j b i for all i = 1, 2, …, m Non-negativity Constraints : x j 0 for all j = 1, 2, … , n.

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4 Resource Allocation Problem (contd.) Linear Programming Formulation: Maximize j=1,n c j x j subject to j=1,n a ij x j b i for all i = 1, 2, …, m x j 0 for all j = 1, 2, … , n. where c
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6417c02 - INTRODUCTION TO LINEAR PROGRAMMING CONTENTS...

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