Find the optimum solution for the following Integer Linear Programming problem using the Cutting Plane Method. Maximum Profit, z = 7x1 + 5x2 Subject to: 3x1 + 4x2 < 25 6x1 + 4x2 < 29 x1, x2 > 0

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section6.3: Capital Budgeting Models
Problem 3P: Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows:...
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2.

Find the optimum solution for the following Integer Linear Programming problem using the Cutting Plane Method.

Maximum Profit, z = 7x1 + 5x2

Subject to:

3x1 + 4x2 < 25

6x1 + 4x2 < 29

x1, x2 > 0

The optimal linear programming tableau is shown in Table 2.

Table/Jadual 2

Basic Variable /

Pembolehubah Asas

Coeficient of /

Koefisien bagi

Solution /

Penyelesaian

 

z

x1

x2

s1

s2

 

z

1

0

0

1/6

112

35 712

x2

0

1

0

1/2

-1/4

14

x1

0

0

1

-1/3

1/3

13

     
3. Solve the problem in Question 2 using the Branch and Bound Method.
     
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9781337406659
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