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Newcor’s steel mill has received an order for 25 tons of steel. The steel must be 5% carbon and 5% molybdenum by weight. The steel is manufactured by combining three types of metal: steel ingots, scrap steel, and alloys. Four steel ingots are available for purchase. The weight (in tons), cost per ton, carbon and molybdenum content of each ingot are given in Table 97. Three types of alloys can be purchased. The cost per ton and chemical makeup of each alloy are given in Table 98.Steel scrap may be purchased at a cost of $100 per ton. Steel scrap contains 3% carbon and 9% molybdenum. Formulate a mixed integer programming problem whose solution will tell Newcor how to minimize the cost of filling their order.

Newcor’s steel mill has received an order for 25 tons of steel. The steel must be 5% carbon and 5% molybdenum by weight. The steel is manufactured by combining three types of metal: steel ingots, scrap steel, and alloys. Four steel ingots are available for purchase. The weight (in tons), cost per ton, carbon and molybdenum content of each ingot are given in Table 97. Three types of alloys can be purchased. The cost per ton and chemical makeup of each alloy are given in Table 98.Steel scrap may be purchased at a cost of $100 per ton. Steel scrap contains 3% carbon and 9% molybdenum. Formulate a mixed integer programming problem whose solution will tell Newcor how to minimize the cost of filling their order.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Newcor’s steel mill has received an order for 25 tons
of steel. The steel must be 5% carbon and 5% molybdenum
by weight. The steel is manufactured by combining three
types of metal: steel ingots, scrap steel, and alloys. Four
steel ingots are available for purchase. The weight (in tons),
cost per ton, carbon and molybdenum content of each ingot
are given in Table 97.
Three types of alloys can be purchased. The cost per ton
and chemical makeup of each alloy are given in Table 98.Steel scrap may be purchased at a cost of $100 per ton.
Steel scrap contains 3% carbon and 9% molybdenum.
Formulate a mixed integer programming problem whose
solution will tell Newcor how to minimize the cost of filling
their order.

**Table 98: Alloy Composition and Cost Analysis** | **Alloy** | **Cost per Ton ($)** | **Carbon (%)** | **Molybdenum (%)** | |-----------|----------------------|----------------|---------------------| | 1 | 500 | 8 | 6 | | 2 | 450 | 7 | 7 | | 3 | 400 | 6 | 6 | *Description:* This table presents data on three types of alloys, detailing their cost per ton and their composition percentages of carbon and molybdenum. - **Alloy 1** has the highest cost per ton at $500, with 8% carbon and 6% molybdenum. - **Alloy 2** costs $450 per ton, with a composition of 7% carbon and 7% molybdenum. - **Alloy 3** is the least expensive at $400 per ton, consisting of 6% carbon and 6% molybdenum. This table is useful for understanding the trade-offs between the cost and composition of different alloys.
Transcribed Image Text:**Table 98: Alloy Composition and Cost Analysis** | **Alloy** | **Cost per Ton ($)** | **Carbon (%)** | **Molybdenum (%)** | |-----------|----------------------|----------------|---------------------| | 1 | 500 | 8 | 6 | | 2 | 450 | 7 | 7 | | 3 | 400 | 6 | 6 | *Description:* This table presents data on three types of alloys, detailing their cost per ton and their composition percentages of carbon and molybdenum. - **Alloy 1** has the highest cost per ton at $500, with 8% carbon and 6% molybdenum. - **Alloy 2** costs $450 per ton, with a composition of 7% carbon and 7% molybdenum. - **Alloy 3** is the least expensive at $400 per ton, consisting of 6% carbon and 6% molybdenum. This table is useful for understanding the trade-offs between the cost and composition of different alloys.
**Table 97: Metallurgical Analysis of Ingots** This table provides an overview of four different ingots with details including their weight, cost per ton in dollars, and the percentage composition of carbon and molybdenum. | Ingot | Weight (tons) | Cost per Ton ($) | Carbon % | Molybdenum % | |-------|---------------|------------------|----------|--------------| | 1 | 5 | 350 | 5 | 3 | | 2 | 3 | 330 | 4 | 3 | | 3 | 4 | 310 | 5 | 4 | | 4 | 6 | 280 | 3 | 4 | **Explanation:** - **Ingot 1**: Weighs 5 tons, costs $350 per ton, with 5% carbon and 3% molybdenum. - **Ingot 2**: Weighs 3 tons, costs $330 per ton, containing 4% carbon and 3% molybdenum. - **Ingot 3**: Weighs 4 tons, costs $310 per ton, with 5% carbon and 4% molybdenum. - **Ingot 4**: Weighs 6 tons, costs $280 per ton, containing 3% carbon and 4% molybdenum. This data assists in cost analysis and selection for specific metallurgical applications based on composition requirements.
Transcribed Image Text:**Table 97: Metallurgical Analysis of Ingots** This table provides an overview of four different ingots with details including their weight, cost per ton in dollars, and the percentage composition of carbon and molybdenum. | Ingot | Weight (tons) | Cost per Ton ($) | Carbon % | Molybdenum % | |-------|---------------|------------------|----------|--------------| | 1 | 5 | 350 | 5 | 3 | | 2 | 3 | 330 | 4 | 3 | | 3 | 4 | 310 | 5 | 4 | | 4 | 6 | 280 | 3 | 4 | **Explanation:** - **Ingot 1**: Weighs 5 tons, costs $350 per ton, with 5% carbon and 3% molybdenum. - **Ingot 2**: Weighs 3 tons, costs $330 per ton, containing 4% carbon and 3% molybdenum. - **Ingot 3**: Weighs 4 tons, costs $310 per ton, with 5% carbon and 4% molybdenum. - **Ingot 4**: Weighs 6 tons, costs $280 per ton, containing 3% carbon and 4% molybdenum. This data assists in cost analysis and selection for specific metallurgical applications based on composition requirements.
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