A firm has $4$ plants that produce widgets. Plants A$,$ B$,$ and C can each produce $100$ widgets per day. Plant D can produce $50$ widgets per day. Each day, the widgets produced in the plants must be shipped to satisfy the demand of $3$ customers. Customer $1$ requires $75$ units per day, customer $2$ requires $100$ units per day, and customer $3$ requires $175$ units per day. The shipping costs per widget for each possible route are shown in the table below:

Customer

Plant $123$

A $$25$ $$35$ $$15$

B $$20$ $$30$ $$40$

C $$40$ $$35$ $$20$

D $$15$ $$20$ $$25$

The firm needs to satisfy all demand each day, but would like to minimize the total costs.

Which of the following constraints is unnecessary for this problem $($xi$,$j is the number of widgets shipped from factory i to customer j$)?$