OR_AUA_HW5 - IE230 Operations Research I : Homework #5 due...

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IE230 Operations Research I ::::: Homework #5 due Wednesday, 22 March 2006 1. Linear Programming Model Formulation: Brady Corporation produces cabinets. Each week, they require 90,000 cu ft of processed lumber. They may obtain processed lumber in two ways. First, they may purchase lumber from an outside supplier and then dry it at their kiln. Second, they may chop down logs on their own land, cut them into lumber at their sawmill, and finally dry the lumber at their kiln. Brady can purchase grade 1 or grade 2 lumber. Grade 1 lumber costs $3 per cu ft (cubic foot) and when dried yields 0.7 cu ft of useful lumber. Grade 2 lumber costs $7 per cu ft and when dried yields 0.9 cu ft of useful lumber. It costs the company $3 per cu ft to chop down a log. After being cut and dried, one cubic foot of log yields 0.8 cu ft of lumber. Brady incurs costs of $4 per cu ft of lumber that is dried in their kiln. It costs $2.50 per cu ft of logs sent through their 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 cubic foot of grade 1 lumber, grade 2 lumber, or logs is as follows: grade 1: 2 seconds grade 2: 0.8 seconds log: 1.3 seconds a. Formulate an LP to help Brady minimize the weekly cost of meeting the demand for
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OR_AUA_HW5 - IE230 Operations Research I : Homework #5 due...

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