The Rightsize Furniture Company manufactures desks, tables, and chairs. The manufacture of each type of furniture requires lumber and two types of skilled labors to do finishing and carpentry work. The amount of each resource needed to make each type of furniture is given below. Currently, 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. The company believes that demand for desks and chairs is unlimited, but at most 5 tables could be sold. Resource requirments for Rightsize Furniture Resource Desk Table Chair Board feet of lumber 8 6 1 Finishing hours 4 2 1.5 Carpentry hours 2 1.5 0.5 Denote the decision variables as X1, X2, and X3 units of desks, tables, and chairs to be produced, formulate a linear programming (LP) model aimed to maximize the total revenue for the company under resource constraints. Solve for the LP using the Simplex Method by showing all iteration steps.
The Rightsize Furniture Company manufactures desks, tables, and chairs. The manufacture of each type of furniture requires lumber and two types of skilled labors to do finishing and carpentry work. The amount of each resource needed to make each type of furniture is given below. Currently, 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. The company believes that demand for desks and chairs is unlimited, but at most 5 tables could be sold.
Resource requirments for Rightsize Furniture
|
Resource |
Desk |
Table |
Chair |
|
Board feet of lumber |
8 |
6 |
1 |
|
Finishing hours |
4 |
2 |
1.5 |
|
Carpentry hours |
2 |
1.5 |
0.5 |
Denote the decision variables as X1, X2, and X3 units of desks, tables, and chairs to be produced, formulate a linear programming (LP) model aimed to maximize the total revenue for the company under resource constraints.
Solve for the LP using the Simplex Method by showing all iteration steps.
Step by step
Solved in 2 steps
