The Dakota Furniture company manufactures desks, tables, and chairs. The manufacture of each type of furniture requires lumber and two types of skilled labor: furnishing and carpentry. The amount of each resource needed to make each type of furniture is given as follows: Resource Desk Table chair
Lumber (bd ft)
inishing hrs Carpentry hrs 1.5 0.5 1.5 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, XI = # Desks, X2 = # Tables, X3 = # Chairs, Max 60x1 30x2+20x3 S. T 8x1 + 6x2 + x3 <= 48 4x1 + 2x2+ 1.5x3 <= 20 2x1 + 1.5x2 + 0.5x3 <= 8 x2 <=5 x1, x2, x3 20 Lumber (bd ft) Finishing (hrs) Carpentry (hrs) Tables demand Value Reduced Cost Original Val Lower Bound Upper Bound Variable X1 X2 30 20 56 -Infinity 15 35 22.5 Dual Value Slack/Surplus Original Val Lower Bound Upper Bound Infinity 24 10 Infinity 24 24 16 6.6667 nishing Tables demand Use the POM-QM output to provide an answer to each of the following questions: 10 10 20