How to formulate constraints in zero-one linear programming There is a factory which produces 5 types of ice cream. If the $i_{th}$ ice cream is produced then $b_i=1$ otherwise $b_i=0$

How can I express the following constraints:


The simultaneous production of all 5 types ice cream is not possible
The type 1 and type 2 must be either both produced or none be produced ($b1 \oplus b2$)
If type 4 is produced, type 5 must be produced too, but if type 4 isn't produced, type 5 can be produced or not.
If type 4 isn't produced, type 5 must not be produced, otherwise, if type 4 is produced, type 5 can be produced or not
$b_1+b_2+b_3+b_4+b_5 \le 4$
$b_1-b_2=0$
$b_4- b_5 \le 0$
$b_5- b_4 \le 0$