Based on Carino and Lenoir (1988). BradyCorporation produces cabinets. Each week, Bradyrequires 90,000 cubic feet of processed lumber. Thecompany can obtain lumber in two ways. First, itcan purchase lumber from an outside supplier andthen dry it at the Brady kiln. Second, Brady canchop down trees on its land, cut them into lumber atits sawmill, and then dry the lumber at its kiln. Thecompany can purchase grade 1 or grade 2 lumber.Grade 1 lumber costs $3 per cubic foot and whendried yields 0.7 cubic foot of useful lumber. Grade 2lumber costs $7 per cubic foot and when dried yields0.9 cubic foot of useful lumber. It costs the company$3 to chop down a tree. After being cut and dried,a log yields 0.8 cubic feet of lumber. Brady incurscosts of $4 per cubic foot of lumber it dries. It costs$2.50 per cubic foot of logs sent through the sawmill.Each week, the sawmill can process up to 35,000cubic feet of lumber. Each week, up to 40,000 cubicfeet of grade 1 lumber and up to 60,000 cubic feetof 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 isas follows: grade 1, 2 seconds; grade 2, 0.8 second;and log, 1.3 seconds. Determine how Brady canminimize the weekly cost of meeting its demand forprocessed 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 $3 per cubic foot and when
dried yields 0.7 cubic foot of useful lumber. Grade 2
lumber costs $7 per cubic foot and when dried yields
0.9 cubic foot of useful lumber. It costs the company
$3 to chop down a tree. After being cut and dried,
a log yields 0.8 cubic feet of lumber. Brady incurs
costs of $4 per cubic foot of lumber it dries. It costs
$2.50 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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