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# L2_10 - ESI 6314 Deterministic Methods in Operations...

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1/1 ESI 6314 Deterministic Methods in Operations Research Lecture Notes 3 University of Florida Department of Industrial and Systems Engineering / REEF

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2/1 Introduction to Linear Programming
3/1 Resource allocation problem A manufacturing facility makes n products 1 , 2 , . . . , n using m different types of row material, 1 , . . . , m . The cost of one unit of i -th raw material is r i . We have b i units of raw material i available. Producing one unit of product j requires a ij units of raw material i . each unit of product j sells at the price of s j . Decide the production quantities of each product to maximize the total profit.

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4/1 Resource allocation problem Indices : i will be used for the i -th raw material, i = 1 , . . . , m ; j will be used for the j -th product, j = 1 , . . . , n . The decision variables : x j = the number of units of product j to manufacture, j = 1 , . . . , n .
5/1 Resource allocation problem The objective function (maximize the total profit): Cost of raw material i needed to manufacture of one unit of product j is given by a ij r i .

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L2_10 - ESI 6314 Deterministic Methods in Operations...

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