Consider $$\text{max} \ 5x_1+3x_2$$ $$s.t.\ 2x_1+x_2\le 8$$ $$3x_1+2x_2\ge 6$$ $$x_1,x_2\ge0$$
Change the objective function by another function such that the resulting program has infinite optimal solutions.
Any hint please?
How will I solve this?
2026-02-22 22:49:27.1771800567
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How to find infinite optimal solutions for linear program?
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You can visualize this very nicely, see https://www.desmos.com/calculator/jiukwzxdxt
If you change the objective function so that its contour lines are perpendicular to one of the edges of the feasible region, you also get infinitely many solutions.
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Make the objective function a constant and every feasible point is an optimal solution.
Remark: You still have to prove that the feasible set has infinitely many points. You might like to use convexity to prove this.