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L01f05

# L01f05 - Chapter 1 An Introduction 1 Beginning With an...

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Chapter 1: An Introduction 1 Chek Beng Chua Beginning With an Example The Orange Factory Problem Factory produces two products: Frozen concentrate and Orange juice . Each unit of requires and produces Frozen concentrate 2 units electricity \$2 pro±t 1 unit orange 1 unit water Orange juice 1 unit electricity \$3 pro±t 1 unit orange 1 unit water How much frozen concentrate and orange juice should we produce to maximize pro±t? Daily available resources: 10 units electricity; 6 units oranges; 4 units water.

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Chapter 1: An Introduction 2 Chek Beng Chua Decision variables x 1 x 2 denote daily production of frozen concentrate orange juice In summary, Frozen concentrate Orange juice Resource limit Decision variable x 1 x 2 Pro±t 2 3 Electricity 2 1 10 Oranges 1 1 6 Water - 1 1 4 Mathematical model (Eq (1.1) on Pg 8) maximize 2 x 1 + 3 x 2 subject to 2 x 1 + x 2 10 x 1 + x 2 6 - x 1 + x 2 4 x 1 , x 2 0 x 1 and x 2 need not be integers.
Chapter 1: An Introduction 3 Chek Beng Chua

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L01f05 - Chapter 1 An Introduction 1 Beginning With an...

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