INEN 622: Group Quiz 3
Quiz is closed book and notes.
Turn in quiz as a group.
1. (10 pts) Perform one iteration
of the Revised Simplex Method on the cutting stock problem where the raw width
is 15 ft and you want 10 finals of width 3 ft, 20 finals of width 5 ft, and 15
finals of width 8 ft.
2. (10 pts) Perform one iteration
of the Revised Simplex Method on the cutting stock problem where the raw width
is 15 ft and you want 15 finals of width 4 ft, 20 finals of width 6 ft, and 20
finals of width 7 ft.
3. (10 pts) Perform one iteration
of the Revised Simplex Method on the Dantzig-Wolfe
decomposition for following LP where the first constraint makes up A¢ and where the slack variable for the first constraint
and the origin extreme point correspond to the initial basic variables:
Max 3x1
+ 5x2 + 2x3 + 3x4
s.t. 2x1
+ 4x2 + 5x3 + 2x4 £ 7
2x1 + 3x2 £ 6
x1 + 4x2 £ 4
-3x3 - 4x4
£ -12
x3 £ 4
x4 £ 3
x1,
x2, x3, x4 ³ 0
4. (10 pts) Perform one iteration
of the Revised Dual Simplex Method on the following LP:
Min 60x1
+ 10x2 + 20x3
s.t. 3x1
+ x2 + x3 ³ 5
x1 - x2 + x3
³ -1
x1
+ 2x2 - x3 ³ 1
x1,
x2, x3 ³ 0
5. (10 pts) Perform one iteration of the Revised Simplex
Method on the Dantzig-Wolfe decomposition for
following LP where the first three constraints make up A¢ and where the slack variables for the first and third
constraints, the extreme direction wT=(0 0 1 0 0),
and the origin extreme point correspond to the initial basic variables:
Max 6x1
+ 4x2 + 3x3 + 3x4
s.t. x1 + x2 + x5
£ 3
-x2
+ x3 + x4 – x5 £ 5
x1
+ x2 + x3 £ 6
2x1 + x2 £ 4
x4 + x5 £ 3
x4 + 2x5
£ 4
x1,
x2, x3, x4, x5 ³ 0
6. (10 pts) Perform one iteration
of the Revised Simplex Method for bounded variables on the following LP problem
using a solution by setting x2, x5 and x6 at
their upper bound, setting x4 at its lower bound, and setting x1
and x3 as basic variables.
Max 3x1
- 5x2 + x3 + 2x4 + x6
s.t. x1
+ 2x2 + x3 + x4 + x6 = 8
2x1+ x2
- x3 + x5 + x6 = 3
x1 £ 4
-2 £ x2 £ 3
x3 £ 2
0 £ x4
x5 £ 0
0 £ x6 £ 4