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
$
20,000
per hour, and the operating cost of the second mine is
$
14,000
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?
