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The Osgood county refuse department runs two recycling centers. Center 1 costs $40 to run for an eight hour day. In a typical day, 140 pounds of glass and 60 pounds of aluminum are deposited at Center 1. Center 2 costs $50 for an eight hour day, with 100lbs of glass and 180lbs of aluminum deposited per day. The county has a commitment to deliver at least 1540lbs of glass and 1440lbs of aluminum per week. How many days per week should the county open each center to minimize its cost and still meet the requirements?

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Answer:

Center 1 should be open 7 days a week, and center 2 should be open 6 days a week. Total cost = $580

Explanation:

minimize the following equation 40A + 50B

where:

A = center 1

B = center 2

constraints:

140A + 100B ≥ 1540

60A + 180B ≥ 1440

A ≤ 7

B ≤ 7

A, B ≥ 0

using Solver, the optimal solution is 7A + 6B = 580

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