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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
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  • $b_1+b_2+b_3+b_4+b_5 \le 4$
  • $b_1-b_2=0$
  • $b_4- b_5 \le 0$
  • $b_5- b_4 \le 0$
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