# Solved Question: Buckeye Furniture produces tables and chairs, earning \$120 profit

## Description

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.

Which of the following would be a necessary constraint in the problem?

X1 + X2 ≤ 40

X1 + X2 ≤ 200

X1 + X2 ≤ 180

120X1 + 80X2 ≤ 1000

X1=Number of tables

X2=Number of chairs

Objective function:

Maximize Z =\$120*X1+\$80*X2

Constraints:

• Assembly time available per week=200 hours
• Finishing time available per week=180 hours
• Inspection time available= 40 hours

Total Assembly hours required=3X1+2X2 ≤ 200

Total Finishing hours required=2X1+2X2≤ 180

Total Inspection hours required=X1+X2≤ 40