Brady Corporation produces cabinets. Each week, itrequires 90,000 cu ft of processed lumber. The companymay obtain lumber in two ways. First, it may purchaselumber from an outside supplier and then dry it in thesupplier’s kiln. Second, it may chop down logs on its ownland, cut them into lumber at its sawmill, and finally dry thelumber in its own kiln. Brady can purchase grade 1 or grade2 lumber. Grade 1 lumber costs $3 per cu ft and when driedyields 0.7 cu ft of useful lumber. Grade 2 lumber costs $7per cubic foot and when dried yields 0.9 cu ft of usefullumber. It costs the company $3 to chop down a log. Afterbeing cut and dried, a log yields 0.8 cu ft of lumber. Bradyincurs costs of $4 per cu ft of lumber dried. It costs $2.50per cu ft of logs sent through the sawmill. Each week, thesawmill can process up to 35,000 cu ft of lumber. Eachweek, up to 40,000 cu ft of grade 1 lumber and up to 60,000cu ft of grade 2 lumber can be purchased. Each week, 40hours of time are available for drying lumber. The time ittakes to dry 1 cu ft of grade 1 lumber, grade 2 lumber, orlogs is as follows: grade 1—2 seconds; grade 2—0.8 second;log—1.3 seconds. Formulate an LP to help Brady minimizethe weekly cost of meeting the demand for processed lumber.
Brady Corporation produces cabinets. Each week, it
requires 90,000 cu ft of processed lumber. The company
may obtain lumber in two ways. First, it may purchase
lumber from an outside supplier and then dry it in the
supplier’s kiln. Second, it may chop down logs on its own
land, cut them into lumber at its sawmill, and finally dry the
lumber in its own kiln. Brady can purchase grade 1 or grade
2 lumber. Grade 1 lumber costs $3 per cu ft and when dried
yields 0.7 cu ft of useful lumber. Grade 2 lumber costs $7
per cubic foot and when dried yields 0.9 cu ft of useful
lumber. It costs the company $3 to chop down a log. After
being cut and dried, a log yields 0.8 cu ft of lumber. Brady
incurs costs of $4 per cu ft of lumber dried. It costs $2.50
per cu ft of logs sent through the sawmill. Each week, the
sawmill can process up to 35,000 cu ft of lumber. Each
week, up to 40,000 cu ft of grade 1 lumber and up to 60,000
cu ft of grade 2 lumber can be purchased. Each week, 40
hours of time are available for drying lumber. The time it
takes to dry 1 cu ft of grade 1 lumber, grade 2 lumber, or
logs is as follows: grade 1—2 seconds; grade 2—0.8 second;
log—1.3 seconds. Formulate an LP to help Brady minimize
the weekly cost of meeting the demand for processed lumber.
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