Buckeye Furniture produces tables and chairs earning 120 pro

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

Solution

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 <= 200

Finishing hours

2X1 + 2X2 <= 180

Inspection hours

X1 + X2 <= 40

Non-negative Constraint (proportion cannot be negative)

X1, X2 >= 0

X1 and X2 values

Resource requirement

Assembly hours

Finishing hours

Inspection hours

X1 = 70, X2 = 0

3(70)+2(0)= 140

< 200, feasible

2(70)+2(0)=140

<180, feasible

(70)+(0)=70

> 40, infeasible

Solution is infeasible

X1 = 0, X2 =5 0

3(0)+2(50)= 100

< 200, feasible

2(0)+2(50)=100

<180, feasible

(0)+(50)=50

> 40, infeasible

Solution is infeasible

X1 = 25, X2 = 25

3(25)+2(25)= 120

< 200, feasible

2(25)+2(25)=100

<180, feasible

(25)+(25)=50

> 40, infeasible

Solution is infeasible

X1 = 0, X2 = 0

3(0)+2(0)= 0

< 200, feasible

2(0)+2(0)=0

<180, feasible

(0)+(0)=0

< 40, feasible

Solution is feasible

Correct ANS: X1 =0, X2 = 0

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