Consider the linear programming problem: max {x1 + x2 + x3}
subject to constraints
x1 + x2 - x3 ≤ 1
x1 + x3 ≤ 2
0 ≤ x1 ≤ \(\frac{1}{2}\), x2 ≥ 0
and 0 ≤ x3 ≤ 1
Which of the following statements are true?
1
The optimum value is 3
2
The optimum value is \(\frac{3}{2}\)
3
(0, 2, 1) is an extreme point of the feasible region
4
\(\rm \left(\frac{1}{2}, 0, 1\right)\) is the optimal solution