A craft furniture manufacturer produces round kitchen tables (X1) and matching chairs (X2) in its workshop from 600 board feet of oak. Each table requires 30 hours of labor and each chair requires 18 hours, and there are 480 hours of labor available. Each table requires 40 board feet and each chair requires 15 board feet. A table provides $575 in profit and each chair provides $120 in profit. In the integer programming model formulation for this problem, if each table requires 6 chairs to go with it, but additional chairs can be made and sold separately, this constraint, in proper form for computer solution, could be written as:Group of answer choices6X1 + X2 0X1 + 6X2 06X1 – X2 0X1 + X2 6
Question
A craft furniture manufacturer produces round kitchen tables (X1) and matching chairs (X2) in its workshop from 600 board feet of oak. Each table requires 30 hours of labor and each chair requires 18 hours, and there are 480 hours of labor available. Each table requires 40 board feet and each chair requires 15 board feet. A table provides 120 in profit. In the integer programming model formulation for this problem, if each table requires 6 chairs to go with it, but additional chairs can be made and sold separately, this constraint, in proper form for computer solution, could be written as:Group of answer choices6X1 + X2 0X1 + 6X2 06X1 – X2 0X1 + X2 6
Solution
The constraint, in proper form for computer solution, could be written as: 6X1 - X2 ≤ 0. This is because for every table (X1) produced, there must be at least 6 chairs (X2). If additional chairs are made and sold separately, the number of chairs (X2) could be greater than 6 times the number of tables (X1), but not less. Therefore, 6X1 - X2 should be less than or equal to 0.
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