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 420 tons of regular - grade and 520 tons of low-grade ore per week. The first mine produces 6 tons of regular - grade and 18 tons of low-grade ore per hour. The second mine produces 18 tons of regular - grade and 9 tons of low-grade ore per hour. The operating cost of the first mine is $7000 per hour, and the operating cost of the second mine is $ 22,000 per hour. The first mine can be operated no more than 37 hours a week, and the second mine can be operated no more than 28 hours a week. How many hours per week should each mine be operated to minimize the cost?
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 420 tons of regular - grade and 520 tons of low-grade ore per week. The first mine produces 6 tons of regular - grade and 18 tons of low-grade ore per hour. The second mine produces 18 tons of regular - grade and 9 tons of low-grade ore per hour. The operating cost of the first mine is $7000 per hour, and the operating cost of the second mine is $ 22,000 per hour. The first mine can be operated no more than 37 hours a week, and the second mine can be operated no more than 28 hours a week. How many hours per week should each mine be operated to minimize the cost?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.1: Solution Of Linear Systems
Problem 56E
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Transcribed Image Text: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 420 tons of regular
- grade and 520 tons of low-grade ore per week.
The first mine produces 6 tons of regular - grade
and 18 tons of low-grade ore per hour. The
second mine produces 18 tons of regular - grade
and 9 tons of low-grade ore per hour. The
operating cost of the first mine is $7000 per hour,
and the operating cost of the second mine is $
22,000 per hour. The first mine can be operated no
more than 37 hours a week, and the second mine
can be operated no more than 28 hours a week.
How many hours per
week should each mine be
operated to minimize the cost?
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