11. A school is building a teaching building and needs 400 pieces of glass of size A and 500 pieces of glass of size B. The store has two types of glass, A and B. It is known that each piece of type A glass costs 48 yuan and can be cut into 4 pieces of size A and 6 pieces of size B; each piece of type B glass costs 58 yuan and can be cut into 5 pieces of size A and 5 pieces of size B. Therefore, the minimum cost for the school to purchase both types A and B glass is yuan.
11.4720 .

Let the number of glass panels of specifications $A$ and $B$ to be purchased be $x$ and $y$ respectively. The constraints are
$$
\left\{\begin{array}{l}
x \geqslant 0, y \geqslant 0, \\
4 x+5 y \geqslant 400, \\
6 x+5 y \geqslant 500 .
\end{array}\right.
$$

The cost paid by the school $P=48 x+58 y$.