Based on Carino and Lenoir (1988). Brady Corporation produces cabinets. Each week, Brady requires 90,000 cubic feet of processed lumber. The company can obtain lumber in two ways. First, it can purchase lumber from an outside supplier and then dry it at the Brady kiln. Second, Brady can chop down trees on its land, cut them into lumber at its sawmill, and then dry the lumber at its kiln. The company can purchase grade 1 or grade 2 lumber. Grade 1 lumber costs $4 per cubic foot and when dried yields 0.8 cubic foot of useful lumber. Grade 2 lumber costs $10 per cubic foot and when dried yields 0.95 cubic foot of useful lumber. It costs the company $8 to chop down a tree. After being cut and dried, a tree yields 5.0 cubic feet of lumber. Brady incurs costs of $6 per cubic foot of lumber it dries. It costs $6.50 per cubic foot of logs sent through the sawmill. Each week, the sawmill can process up to 35,000 cubic feet of lumber. Each week, up to 40,000 cubic feet of grade 1 lumber and up to 60,000 cubic feet of grade 2 lumber can be purchased. Each week, 40 hours of time are available for drying lumber. The time it takes to dry one cubic foot of lumber is as follows: grade 1, 2 seconds; grade 2, 0.8 second; and log, 1.3 seconds. Determine how Brady can minimize the weekly cost of meeting its demand for processed lumber
Based on Carino and Lenoir (1988). Brady Corporation produces cabinets. Each week, Brady requires 90,000 cubic feet of processed lumber. The company can obtain lumber in two ways. First, it can purchase lumber from an outside supplier and then dry it at the Brady kiln. Second, Brady can chop down trees on its land, cut them into lumber at its sawmill, and then dry the lumber at its kiln. The company can purchase grade 1 or grade 2 lumber. Grade 1 lumber costs $4 per cubic foot and when dried yields 0.8 cubic foot of useful lumber. Grade 2 lumber costs $10 per cubic foot and when dried yields 0.95 cubic foot of useful lumber. It costs the company $8 to chop down a tree. After being cut and dried, a tree yields 5.0 cubic feet of lumber. Brady incurs costs of $6 per cubic foot of lumber it dries. It costs $6.50 per cubic foot of logs sent through the sawmill. Each week, the sawmill can process up to 35,000 cubic feet of lumber. Each week, up to 40,000 cubic feet of grade 1 lumber and up to 60,000 cubic feet of grade 2 lumber can be purchased. Each week, 40 hours of time are available for drying lumber. The time it takes to dry one cubic foot of lumber is as follows: grade 1, 2 seconds; grade 2, 0.8 second; and log, 1.3 seconds. Determine how Brady can minimize the weekly cost of meeting its demand for processed lumber
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