Solution: If Type A board houses are built with X rooms, then Type B board houses are built with (400-x) rooms.

54x+78(400-x)≤24000。

26x+4 1(400-x)≤ 12000

The solution is x≥300.

And ∵ 0≤x≤400, ∴ ∴300 ≤x≤400. ..

These 400 board houses can accommodate the victims w = 5x+8 (400-x) =-3x+3200.

When x=300, w gets the maximum value of 2300.

A: 400 board rooms can accommodate up to 2,300 people.