Taking x to represent the number of type A and y to represent the number of shirts of type B, write down four inequalities in x and y that satisfy the above information.

Let $x$ be the number of shirts of type A.
Let $y$ be the number of shirts of type B.

"The total number of shirts must not exceed 400."
This means the sum of type A and type B shirts must be less than or equal to 400.

"He has to supply more of type A than of type B."
This means the number of type A shirts must be strictly greater than the number of type B shirts.

"He must supply at most 300 of type A."
This means the number of type A shirts must be less than or equal to 300.

"and at least 80 of type B."
This means the number of type B shirts must be greater than or equal to 80.

The four inequalities are:

1. $x + y \le 400$
2. $x > y$
3. $x \le 300$
4. $y \ge 80$

The four inequalities are: