Question

The Dakota Furniture Company manufactures desks, tables and chairs. The manufacture of each type of furniture requires lumber and two types of skilled labor: finishing and carpentry. The amount of each resource needed to make each type of furniture is given in the table below. Resource | Desk | Table | Chair Lumber (bd ft) | 8 | 6 | 1 Finishing hrs | 4 | 2 | 1.5 Carpentry hrs | 2 | 1.5 | 0.5 At present, 48 board feet of lumber, 20 finishing hours, and 8 carpentry hours are available. A desk sells for $60, a table for $30, and a chair for $20. Dakota believes that the demand for desks and chairs is unlimited, but at most five tables can be sold. The linear programming model that can be used to maximize the company's total profits is given below: Let, X1 = # Desks, X2 = # Tables, X3 = # Chairs, Max 60x1 + 30x2 + 20x3 S.T. 8x1 + 6x2 + x3 <= 48 Lumber (bd ft) 4x1 + 2x2 + 1.5x3 <= 20 Finishing (hrs) 2x1 + 1.5x2 + 0.5x3 <= 8 Carpentry (hrs) x2 <= 5 Tables demand x1, x2, x3 >= 0 Variable | Value | Reduced Cost | Original Val | Lower Bound | Upper Bound X1 | 2 | 0 | 60 | 56 | 80 X2 | 0 | 5 | 30 | -Infinity | 35 X3 | 8 | 0 | 20 | 15 | 22.5 Constraint | Dual Value | Slack/Surplus | Original Val | Lower Bound | Upper Bound Lumber | 0 | 24 | 48 | 24 | Infinity Finishing | 10 | 0 | 20 | 16 | 24 Carpentry | 10 | 0 | 8 | 6.6667 | 10 Tables demand | 0 | 5 | 5 | 0 | Infinity Use the POM-QM output to provide an answer to each of the following questions:

          The Dakota Furniture Company manufactures desks, tables and chairs. The manufacture
of each type of furniture requires lumber and two types of skilled labor: finishing and
carpentry. The amount of each resource needed to make each type of furniture is given in
the table below.

Resource | Desk | Table | Chair
Lumber (bd ft) | 8 | 6 | 1
Finishing hrs | 4 | 2 | 1.5
Carpentry hrs | 2 | 1.5 | 0.5

At present, 48 board feet of lumber, 20 finishing hours, and 8 carpentry hours are
available. A desk sells for $60, a table for $30, and a chair for $20. Dakota believes that
the demand for desks and chairs is unlimited, but at most five tables can be sold. The
linear programming model that can be used to maximize the company's total profits is
given below:
Let,
X1 = # Desks,
X2 = # Tables,
X3 = # Chairs,

Max 60x1 + 30x2 + 20x3
S.T.
8x1 + 6x2 + x3 <= 48    Lumber (bd ft)
4x1 + 2x2 + 1.5x3 <= 20 Finishing (hrs)
2x1 + 1.5x2 + 0.5x3 <= 8 Carpentry (hrs)
x2 <= 5                 Tables demand
x1, x2, x3 >= 0

Variable | Value | Reduced Cost | Original Val | Lower Bound | Upper Bound
X1 | 2 | 0 | 60 | 56 | 80
X2 | 0 | 5 | 30 | -Infinity | 35
X3 | 8 | 0 | 20 | 15 | 22.5
Constraint | Dual Value | Slack/Surplus | Original Val | Lower Bound | Upper Bound
Lumber | 0 | 24 | 48 | 24 | Infinity
Finishing | 10 | 0 | 20 | 16 | 24
Carpentry | 10 | 0 | 8 | 6.6667 | 10
Tables demand | 0 | 5 | 5 | 0 | Infinity

Use the POM-QM output to provide an answer to each of the following questions:

The Dakota Furniture Company manufactures desks, tables and chairs. The manufacture
of each type of furniture requires lumber and two types of skilled labor: finishing and
carpentry. The amount of each resource needed to make each type of furniture is given in
the table below.

Resource | Desk | Table | Chair
Lumber (bd ft) | 8 | 6 | 1
Finishing hrs | 4 | 2 | 1.5
Carpentry hrs | 2 | 1.5 | 0.5

At present, 48 board feet of lumber, 20 finishing hours, and 8 carpentry hours are
available. A desk sells for 60, a table for30, and a chair for 20. Dakota believes that
the demand for desks and chairs is unlimited, but at most five tables can be sold. The
linear programming model that can be used to maximize the company's total profits is
given below:
Let,
X1 = # Desks,
X2 = # Tables,
X3 = # Chairs,

Max 60x1 + 30x2 + 20x3
S.T.
8x1 + 6x2 + x3 <= 48 Lumber (bd ft)
4x1 + 2x2 + 1.5x3 <= 20 Finishing (hrs)
2x1 + 1.5x2 + 0.5x3 <= 8 Carpentry (hrs)
x2 <= 5 Tables demand
x1, x2, x3 >= 0

Variable | Value | Reduced Cost | Original Val | Lower Bound | Upper Bound
X1 | 2 | 0 | 60 | 56 | 80
X2 | 0 | 5 | 30 | -Infinity | 35
X3 | 8 | 0 | 20 | 15 | 22.5
Constraint | Dual Value | Slack/Surplus | Original Val | Lower Bound | Upper Bound
Lumber | 0 | 24 | 48 | 24 | Infinity
Finishing | 10 | 0 | 20 | 16 | 24
Carpentry | 10 | 0 | 8 | 6.6667 | 10
Tables demand | 0 | 5 | 5 | 0 | Infinity

Use the POM-QM output to provide an answer to each of the following questions:

Added by Manuel W.

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