Consider the following mixed-integer linear program: Max 1x₁ + 1x2 s.t. 7x₁ + 9x₂ ≤ 63 9x1 + 5x₂ ≤ 45 3x₁ + 1x₂ ≤ 12 x1, x2 = 0 and x2 integer a. Graph the constraints for this problem. Indicate on your graph all feasible mixed- integer solutions. b. Find the optimal solution to the LP Relaxation. Round the value of x2 down to find a feasible mixed-integer solution. Specify upper and lower bounds on the value of the optimal solution to the mixed-integer linear program. C. Find the optimal solution to the mixed-integer linear program.
Consider the following mixed-integer linear program: Max 1x₁ + 1x2 s.t. 7x₁ + 9x₂ ≤ 63 9x1 + 5x₂ ≤ 45 3x₁ + 1x₂ ≤ 12 x1, x2 = 0 and x2 integer a. Graph the constraints for this problem. Indicate on your graph all feasible mixed- integer solutions. b. Find the optimal solution to the LP Relaxation. Round the value of x2 down to find a feasible mixed-integer solution. Specify upper and lower bounds on the value of the optimal solution to the mixed-integer linear program. C. Find the optimal solution to the mixed-integer linear program.
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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
Transcribed Image Text:Consider the following mixed-integer linear program:
Max 1x₁ + 1x₂
s.t.
7x₁ + 9x₂ ≤ 63
=
9x15x₂45
3x₁ + 1x₂ ≤ 12
X1, X20 and x2 integer
a.
Graph the constraints for this problem. Indicate on your graph all feasible mixed-
integer solutions.
b.
Find the optimal solution to the LP Relaxation. Round the value of x2 down to find a
feasible mixed-integer solution. Specify upper and lower bounds on the value of the
optimal solution to the mixed-integer linear program.
C. Find the optimal solution to the mixed-integer linear program.
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