The straight line l:y=kx+b intersects with point c (1, 1), so 1=k+b, so b =1-K. The straight line l: y = kx+1-K.

The abscissa of the intersection m of straight line AB:x+y= 1 and straight line l:y=kx+ 1-k is 1/( 1+k).

The line l:y=kx+ 1-k intersects the y axis at n (0, 1-k).

Therefore, the area of △BMN is s = (1/2) × bn×1/(1+k) = k/2 (1+k).

△△BMN area S=k/2( 1+k)≤ 1/4.

Maximum value of s

1/4