How can i solve this problem?
$$\max_{a,b,c,d\in\Bbb R} \sqrt{a^2+(3-b)^2}+\sqrt{(b-c)^2+1}+\sqrt{c^2+(1-d)^2}$$ \begin{align*} \text{subject to: }&\qquad 0 \le a \le 1, \quad 1 \le b \le 2,\quad 1 \le c \le b,\quad 0 \le d \le 1 \\ &\sqrt{a^2+(3-b)^2} \le \sqrt{(1-a)^2+(3-c)^2}\quad \text{and}\quad \sqrt{c^2+(1-d)^2} \le \sqrt{d^2+b^2}\end{align*}
Solve the unconstrained problem which leads to
$$ a=0, \;\;\; b=3, \;\;\; c=0, \;\;\; d=1, \;\;\; $$
and notice that the only constraint that is violated is $b \le 2$.
Then, solve the problem with only this constraint which leads to
$$ a=0, \;\;\; b=2, \;\;\; c=0, \;\;\; d=1, \;\;\; $$
and notice that none of the constraints is violated.