# How to find infinite optimal solutions for linear program?

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.

How will I solve this?

• Let the objective function be a constant, say $0$, $1$, or even $\pi$. That is every point is equally optimal. – Siong Thye Goh Feb 4 '18 at 8:02
• $\max 0x_1+0x_2$. – Siong Thye Goh Feb 4 '18 at 18:04