A small furniture manufactuere produces fine dining tables and chaires. Each pro

Question

A small furniture manufactuere produces fine dining tables and chaires. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2.5 hours of finishing, and 0.5 hours of inspection. Each chair requires 1.5 hours of assembly, 1 hours of finishing, and 0.25 hours of inspection. The profit per table is $165 while the profirt per chair is $28. Currently, each week there ware 310 hours of assembly time available, 280 hours of finishing time, and 140 hours of inspection time. THe dining table and chair are sold as a set of one table and six chairs. Formulate this as a linear programming problem. Carefully define all decision variables.

Explanation / Answer

Let x be the number of chairs produced and y be the tables A set has 6 chairs and 1 table The objective function is to Maximize 28*6 X + 165 Y Max, 168x + 165y Subject to 9x + 3y 310 (Assembly time constraint) 6x + 2.5y 280 (Finishing time constraint) 1.5x + 0.5y 140 (Inspection time constraint) x,y 0 (Non Negativity Constraint)

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