4x1 + 3x2 5x1 + 7x2 s 35 8x1 + 5x2 s 40 X1, X2 2 0 and x1 integer

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following mixed-integer linear program:
Max
4x1 + 3x2
s.t.
5x1 + 7x2 s 35
8x1 + 5x2 s 40
X1, X2 20 and x1 integer
a. Choose the correct graph which shows the constraints for this problem and uses boldface vertical lines to indicate all feasible mixed-integer solutions.
(i)
(ii)
6.
3-
2-
1.
123
4
6.
7.
9.
10 z1
1
3.
6.
10 z
(ii)
(iv)
6-
4-
4-
3-
3.
2-
2-
14
1+
9 10 z
4
5'
6.
9 10 z1
b. Find the optimal solution to the LP Relaxation. If required, round your answers to two decimal places.
The optimal solution is given by x1 =
,X2 =
Its value is
Round the value of x1 down to find a feasible mixed-integer solution. If required, round your answers to two decimal places.
with a value of
Rounding the value of x1 down to find a feasible mixed integer solution yields x1 =
Is this solution optimal?
No v
Why or why not?
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
Transcribed Image Text:Consider the following mixed-integer linear program: Max 4x1 + 3x2 s.t. 5x1 + 7x2 s 35 8x1 + 5x2 s 40 X1, X2 20 and x1 integer a. Choose the correct graph which shows the constraints for this problem and uses boldface vertical lines to indicate all feasible mixed-integer solutions. (i) (ii) 6. 3- 2- 1. 123 4 6. 7. 9. 10 z1 1 3. 6. 10 z (ii) (iv) 6- 4- 4- 3- 3. 2- 2- 14 1+ 9 10 z 4 5' 6. 9 10 z1 b. Find the optimal solution to the LP Relaxation. If required, round your answers to two decimal places. The optimal solution is given by x1 = ,X2 = Its value is Round the value of x1 down to find a feasible mixed-integer solution. If required, round your answers to two decimal places. with a value of Rounding the value of x1 down to find a feasible mixed integer solution yields x1 = Is this solution optimal? No v Why or why not? The input in the box below will not be graded, but may be reviewed and considered by your instructor.
4-
4-
3-
3-
2.
2-
1-
1-
4
10 z
89 10 z
(iii)
(iv)
7.
6.
4+
3.
3-
2-
2-
1-
4
6.
10 z
2.
3.
78 9 10 z
b. Find the optimal solution to the LP Relaxation. If required, round your answers to two decimal places.
The optimal solution is given by x1 -
,X2-
Its value is
Round the value of x1 down to find a feasible mixed-integer solution. If required, round your answers to two decimal places.
Rounding the value of x1 down to find a feasible mixed integer solution yields x1 =
X2
with a value of
Is this solution optimal?
No v
Why or why not?
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
C. Find the optimal solution for the mixed-integer linear program. If required, round your answers to two decimal places.
Its value is
Solution details x, =
X2 =
Feedback
T Check My Work
Partially correct
Transcribed Image Text:4- 4- 3- 3- 2. 2- 1- 1- 4 10 z 89 10 z (iii) (iv) 7. 6. 4+ 3. 3- 2- 2- 1- 4 6. 10 z 2. 3. 78 9 10 z b. Find the optimal solution to the LP Relaxation. If required, round your answers to two decimal places. The optimal solution is given by x1 - ,X2- Its value is Round the value of x1 down to find a feasible mixed-integer solution. If required, round your answers to two decimal places. Rounding the value of x1 down to find a feasible mixed integer solution yields x1 = X2 with a value of Is this solution optimal? No v Why or why not? The input in the box below will not be graded, but may be reviewed and considered by your instructor. C. Find the optimal solution for the mixed-integer linear program. If required, round your answers to two decimal places. Its value is Solution details x, = X2 = Feedback T Check My Work Partially correct
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