Buckeye Furniture produces tables and chairs, earning $120 profit per table and

Question

Buckeye Furniture produces tables and chairs, earning $120 profit per table and $80 profit per chair. Each table and chair goes through three stages in the manufacturing process: assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection. Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection. Every week there are 200 hours of assembly time available, 180 hours of finishing time, and 40 hours of inspection time.

The decision variables in the model are X1 for the number of tables and X2 for the number of chairs. All constraints must be in the proper form of a linear equation.

Suppose it is decided that there must be exactly 1 chair produced for every table. Using the proper form of a linear equation, how would this constraint be written?

X1 + X2

X1 – X2 < 1

X1 – X2 = 1

X1 - X2 = 0

Explanation / Answer

Let X1 be the number of tables and X2 be the number of chairs

Based on the objective function

Z=120X1 +80 X2

Constraints on assembly available: 3 X1 +2 X2 < 200

Constraints on finishing available: 2X1 +2 X2 < 180

Constraints on inspection available: 1X1 +1X2 < 40

Constraints on production: 1X1 +1X2

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