7. A company has two mines. Mine A can produce 1 ton of high-grade iron ore, 3 tons of medium-grade iron ore, and 5 tons of low-grade iron ore every day; Mine B can produce 2 tons of each of these three types of iron ore every day. The company's demand for these three types of iron ore is at least 80 tons, 160 tons, and 200 tons respectively. Assume that these two mines each need to spend $2,000 per day to mine iron ore. How many days do these two mines need to mine to meet market demand with the lowest mining cost? (a) Try to define variables for the above problem and establish its linear programming model. (b) Solve the above linear programming problem.

7. A company has two mines. Mine A can produce 1 ton of high-grade iron ore, 3 tons of medium-grade iron ore, and 5 tons of low-grade iron ore every day; Mine B can produce 2 tons of each of these three types of iron ore every day. The company's demand for these three types of iron ore is at least 80 tons, 160 tons, and 200 tons respectively. Assume that these two mines each need to spend $2,000 per day to mine iron ore. How many days do these two mines need to mine to meet market demand with the lowest mining cost? (a) Try to define variables for the above problem and establish its linear programming model. (b) Solve the above linear programming problem.

Name: 7. A company has two mines. Mine A can produce 1 ton of high-gradeiro
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Description: 7. A company has two mines. Mine A can produce 1 ton of high-gradeiron ore, 3 tons of medium-grade iron ore, and 5 tons of low-grade ironore every day; Mine B can produce 2 tons of each of these three typesof iron ore every day . The company's deman

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

7. A company has two mines. Mine A can produce 1 ton of high-grade
iron ore, 3 tons of medium-grade iron ore, and 5 tons of low-grade iron
ore every day; Mine B can produce 2 tons of each of these three types
of iron ore every day . The company's demand for these three types of
iron ore is at least 80 tons, 160 tons, and 200 tons respectively.
Assume that these two mines each need to spend $2,000 per day to
mine iron ore. How many days do these two mines need to mine to
meet market demand with the lowest mining cost?
(a) Try to define variables for the above problem and establish its
linear programming model.
(b) Solve the above linear programming problem.

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A mining company owns two mines. These mines produce an ore that can be graded into two classes: regular grade and low grade. The company must produce at least 410 tons of regular-grade and 530 tons of low-grade ore per week. The first mine produces 6 tons of regular-grade and 16 tons of low-grade ore per hour. The second mine produces 20 tons of regular-grade and 10 tons of low-grade ore per hour. The operating cost of the first mine is $9000 per hour, and the operating cost of the second mine is $30,500 per hour. The first mine can be operated no more than 55 hours a week, and the second mine can be operated no more than 29 hours a week. How many hours per week should each mine be operated to minimize the cost? First Mine: __ hours Second Mine:__ hours
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