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
Answer:
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
Answer:
X1 + X2 ≤ 40
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