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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 answers below is a feasible solution? X1 = 70, X2 = 0 X1 = 0, X2 = 50 X1 = 25, X2 = 25 X1 = 0, X2 = 0 none of the above

Formulation:
Products
Tables (X1)
Chairs (X2)
Profit per unit
$120
$80
Resource
Resource required per unit of product
Maximum resource available
Assembly
3 hours
2 hours
200 hours per week
Finishing
2 hours
2 hours
180 hours per week
Inspection
1 hours
1 hours
40 hours per week
Decision Variables
X1 = Number of tables to be produced
X2 = Number of chairs to be produced
Objective Function
The objective is to minimize the total cost of blending:
Max Z = $120X1 + $80X2
Subject to:
Assembly hours
3X1 + 2X2 = 0
X1 and X2 values
Resource requirement
Assembly hours
Finishing hours
Inspection hours
X1 = 70, X2 = 0
3(70)+2(0)= 140
40, infeasible
Solution is infeasible
X1 = 0, X2 =5 0
3(0)+2(50)= 100
40, infeasible
Solution is infeasible
X1 = 25, X2 = 25
3(25)+2(25)= 120
40, infeasible
Solution is infeasible
X1 = 0, X2 = 0
3(0)+2(0)= 0

 
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