A group of fresh industrial engineering graduates in the Sultanate of Oman are starting their own business, specializing in the production of two types of metal ingots, I and II. They are eager to apply what they learned in their Theory of Modeling and Optimization course to solve a real-world problem. The graduates operate a foundry that smelts steel, aluminum, and cast-iron scraps. The ingots have specific limits on the aluminum, graphite, and silicon contents. To meet these specifications, aluminum and silicon briquettes may be used in the smelting process. The problem is to determine the optimal blending of input materials that satisfies the demand requirements at minimum cost. This involves deciding how much of each input material to use in the production of each type of ingot. Input item Steel scrap Aluminum scrap Cast iron scrap Aluminum briquette Silicon briquette Contents (%) Aluminum Graphite 5 1 15 10 95 0 100 0 Ingredient Aluminum Graphite Silicon Demand (tons/day) 0 0 Ingot I (%) Minimum 8.1 1.5 2.5 Silicon 4 2 8 0 100 Maximum 10.8 3.0 130 Cost/ton ($) Available (tons/day) 100 1000 150 500 75 2500 Any amount Any amount 900 380 Ingot II (%) Minimum 6.2 4.1 2.8 250 Maximum 8.9 4.1

A group of fresh industrial engineering graduates in the Sultanate of Oman are starting their own business, specializing in the production of two types of metal ingots, I and II. They are eager to apply what they learned in their Theory of Modeling and Optimization course to solve a real-world problem. The graduates operate a foundry that smelts steel, aluminum, and cast-iron scraps. The ingots have specific limits on the aluminum, graphite, and silicon contents. To meet these specifications, aluminum and silicon briquettes may be used in the smelting process. The problem is to determine the optimal blending of input materials that satisfies the demand requirements at minimum cost. This involves deciding how much of each input material to use in the production of each type of ingot. Input item Steel scrap Aluminum scrap Cast iron scrap Aluminum briquette Silicon briquette Contents (%) Aluminum Graphite 5 1 15 10 95 0 100 0 Ingredient Aluminum Graphite Silicon Demand (tons/day) 0 0 Ingot I (%) Minimum 8.1 1.5 2.5 Silicon 4 2 8 0 100 Maximum 10.8 3.0 130 Cost/ton ($) Available (tons/day) 100 1000 150 500 75 2500 Any amount Any amount 900 380 Ingot II (%) Minimum 6.2 4.1 2.8 250 Maximum 8.9 4.1

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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