Tools › Operations Research › Optimization › Linear Programming › Example
Winston: Dakota Furniture desks, tables and chairs with the LINDO sensitivity report
| Tool | Linear Programming |
| Source | Winston, W. L. (2004). Operations Research: Applications and Algorithms, 4th ed. Thomson Brooks/Cole, Belmont, CA. Sections 4.5, 5.2 and 6.3. |
| Level | Undergraduate |
Problem
Dakota Furniture makes desks (x1, 60 each), tables (x2, 30) and chairs (x3, 20) from 48 board-feet of lumber, 20 finishing hours and 8 carpentry hours (8 x1 + 6 x2 + x3 ≤ 48, 4 x1 + 2 x2 + 1.5 x3 ≤ 20, 2 x1 + 1.5 x2 + 0.5 x3 ≤ 8), and at most 5 tables can be sold. Find the revenue-maximizing plan, the shadow prices, the reduced cost of tables and the allowable ranges.
Inputs to Enter
- max 60 x1 + 30 x2 + 20 x3
- lumber: 8 x1 + 6 x2 + x3 <= 48 ; finishing: 4 x1 + 2 x2 + 1.5 x3 <= 20
- carpentry: 2 x1 + 1.5 x2 + 0.5 x3 <= 8 ; demand: x2 <= 5
Answers
- x1 = 2, x2 = 0, x3 = 8, z = 280
- Shadow prices: lumber 0, finishing 10, carpentry 10, table demand 0; slack lumber 24, slack demand 5
- Reduced cost of x2 = −5
- RHS ranges: finishing [16, 24], carpentry [4 − 4/3, 10], lumber [24, ∞)
- Objective ranges: c1 [56, 80], c2 (−∞, 35], c3 [15, 22.5]
Notes
Type the model in place of the default Wyndor problem. The reduced cost prints as c_j − z_j, so a non-basic variable of a maximization shows a negative value.