‫בס"ד‬
4 ‫תרגיל‬
1 ‫שאלה‬
Use the simplex algorithm to find the optimal solutions to the following LP. Use Lindo to
check your answer.
max z  5 x1  3 x 2  x3
s.t. : x1  x 2  3 x3  6
5 x1  3 x 2  6 x3  15
x1 , x 2 , x3  0
2 ‫שאלה‬
Use the simplex algorithm to find the optimal solutions to the following LP. Use Lindo to
check your answer.
min z  4 x1  x 2
s.t. : 3 x1  x 2  6
 x1  2 x 2  0
x1 , x 2  0
3 ‫שאלה‬
Use the simplex algorithm to find the optimal solutions to the following LP. Use Lindo to
check your answer.
max z  5 x1  x 2
s.t. : x1  3x 2  1
x1  4 x 2  3
x1 , x 2  0
4 ‫שאלה‬
Use the simplex algorithm to find the optimal solutions to the following LP. Use Lindo to
check your answer.
min z   x1  2 x 2
s.t. : 2 x1  x 2  5
x1  x 2  3
x1 , x 2  0
5 ‫שאלה‬
Use the simplex algorithm to find the optimal solutions to the following LP. Use Lindo to
check your answer.
max z  4 x1  5 x 2  9 x3  11x 4
s.t. : 1x1  1x 2  1x3  1x 4  15
7 x1  5 x 2  3 x3  2 x 4  120
3 x1  5 x 2  10 x3  15 x 4  100
x1 , x 2 , x3 , x 4  0
6 ‫שאלה‬
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
Table 4
Resource
Lumber
Finishing hours
Carpentry hours
Table 4
Desk
8 board ft
4
2
Table
6 board ft
2
1.5
Chair
1 board ft
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
demand for desks and chairs is unlimited, but at most five tables can be sold. Since the
available resources have already been purchased, Dakota wants to maximize total
revenue. Solve the problem using Simplex and LINDO.