Consider the following all-integer linear program: Max 5x1 + 8x2 s.t. 5x1 + 5x2 < 32 9x1 + 3x2 < 38 x1 + 2x2 < 12 X1, x2 2 0 and integer a. Choose the correct graph which shows the constraints for this problem and uses dots to indicate all feasible integer solutions. (i) (ii) 5- 4- 3- 2- 1- 6 (iii) (iv) 3- 14 b. Find the optimal solution to the LP Relaxation. If required, round your answers to two decimal places. X1= X2= Optimal Solution to the LP Relaxation Round down to find a feasible integer solution. If your answer is zero enter "0". X1= X2= Feasible integer solution c. Find the optimal integer solution. If your answer is zero enter "0". X1= X2= Optimal Integer Solution Is it the same as the solution obtained in part (b) by rounding down?
Consider the following all-integer linear program: Max 5x1 + 8x2 s.t. 5x1 + 5x2 < 32 9x1 + 3x2 < 38 x1 + 2x2 < 12 X1, x2 2 0 and integer a. Choose the correct graph which shows the constraints for this problem and uses dots to indicate all feasible integer solutions. (i) (ii) 5- 4- 3- 2- 1- 6 (iii) (iv) 3- 14 b. Find the optimal solution to the LP Relaxation. If required, round your answers to two decimal places. X1= X2= Optimal Solution to the LP Relaxation Round down to find a feasible integer solution. If your answer is zero enter "0". X1= X2= Feasible integer solution c. Find the optimal integer solution. If your answer is zero enter "0". X1= X2= Optimal Integer Solution Is it the same as the solution obtained in part (b) by rounding down?
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 all-integer linear program:
Max 5x1 + 8x2
s.t.
5x1 + 5x2 ≤ 32
9x1 + 3x2 ≤ 38
x1 + 2x2 ≤ 12
x1, x2 ≥ 0 and integer
Transcribed Image Text:Consider the following all-integer linear program:
Max
5x1 +
8x2
s.t.
5x1 + 5x2 < 32
9x1 +
3x2 < 38
X1 +
2x2 < 12
X1, x2 2 0 and integer
a. Choose the correct graph which shows the constraints for this problem and uses dots to indicate all feasible integer solutions.
(i)
(ii)
5-
3-
1-
5
6.
1
(iii)
(iv)
54
4-
3
2-
1-
b. Find the optimal solution to the LP Relaxation. If required, round your answers to two decimal places.
X1=
X2%D
Optimal Solution to the LP Relaxation
Round down to find a feasible integer solution. If your answer is zero enter "0".
X1=
X2=
Feasible integer solution
c. Find the optimal integer solution. If your answer is zero enter "0".
X1=
X2=
Optimal Integer Solution
Is it the same as the solution obtained in part (b) by rounding down?
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