Let x be horizontal and y be vertical dimension of the poster.

Then the printed area has dimensions (x-8) cm vertically and (y-10) cm horizontally.


We have these restrictions  

    25 cm <= x-8, y-10 <= 35 cm         (1)

and  

    (x-8)*(y-10) = 781.25 cm^2.         (2)


We want to minimize the product x*y, which is the area of the poster, under restrictions (1) and (2).


From restriction (2), we have

    y - 10 = ,

or

    y =  + 10.              (3)


Then

    xy =  + 10x.


Thus we want to find the minimum of this function 

    Z(x) =  + 10x  under restrictions  25 <= x-8, y-10 <= 35, where y =  + 10.


Doing in accordance with the standard Calculus procedure, we should take the derivative
of function Z(x) and equate it to zero.


It leads us to equation

     + 10 = 0,

from which we get

     = ,   = 625,   x-8 =  = 25,  x = 33 cm,

and (x-8) satisfies the restriction 25 <= x-8 <= 35 cm.


Thus we solved the problem and found that the minimum area of the poster is achieved at x= 25 cm.

Then y =  + 10  by formula (3),  or  y =  + 10 = 41.25.


We see that y satisfies the restriction  25 <= y-10 <= 35 cm.


Thus the answer is: optimum dimensions of the poster are x= 33 cm, y = 41.25 cm;

                    the minimal area of the poster is x*y = 33*41.25 = 1361.25 cm^2.