At Midwest Steel, steel is produced by combining various alloys and scrap pieces of steel in...

 

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At Midwest Steel, steel is produced by combining various alloys and scrap pieces of steel in high-temperature furnaces. For a 100-ton piece of steel, three different alloys and two different types of scrap material are to be used. Each alloy and scrap piece have different properties and chemical makeups. The various characteristics of each alloy and scrap are given below, as well as their availability and cost per ton. Alloy 1 Alloy 2 Alloy 3 Scrap 1 Scrap 2 Carbon Nickel 1.75% 2.0% 2.45% 3.0% 2.80% 4.0% 3.10% 4.5% 3.50% 5.5% Characteristics (per ton) Tensile Chromium Strength 3.5% 0.8% 1.2% 3.9% 2.8% 60,000 40,000 90,000 120,000 70,000 Availability 50 50 20 30 40 Cost $150 $120 $80 $35 $20 The customer wants this produced steel to meet the following chemical re- quirements: the carbon composition must be between 2% and 3%, the nickel composition cannot exceed 4%, the chromium composition must be between 1.3% and 2.7%, and its tensile strength must be between 50,000 and 80,000 psi. Assuming that tensile strength of the produced steel is a weighted average of the tensile strength of each alloy and scrap piece, determine how Midwest can produce this 100-ton piece of steel at minimum cost. At Midwest Steel, steel is produced by combining various alloys and scrap pieces of steel in high-temperature furnaces. For a 100-ton piece of steel, three different alloys and two different types of scrap material are to be used. Each alloy and scrap piece have different properties and chemical makeups. The various characteristics of each alloy and scrap are given below, as well as their availability and cost per ton. Alloy 1 Alloy 2 Alloy 3 Scrap 1 Scrap 2 Carbon Nickel 1.75% 2.0% 2.45% 3.0% 2.80% 4.0% 3.10% 4.5% 3.50% 5.5% Characteristics (per ton) Tensile Chromium Strength 3.5% 0.8% 1.2% 3.9% 2.8% 60,000 40,000 90,000 120,000 70,000 Availability 50 50 20 30 40 Cost $150 $120 $80 $35 $20 The customer wants this produced steel to meet the following chemical re- quirements: the carbon composition must be between 2% and 3%, the nickel composition cannot exceed 4%, the chromium composition must be between 1.3% and 2.7%, and its tensile strength must be between 50,000 and 80,000 psi. Assuming that tensile strength of the produced steel is a weighted average of the tensile strength of each alloy and scrap piece, determine how Midwest can produce this 100-ton piece of steel at minimum cost.

Answer rating: 100% (QA)

Answer Given Data Alloy 1 Alloy 2 Alloy 3 Scrap 1 Scrap 2 Carbon To fin... View the full answer