They want you to minimize

    f(x,y) = (x+6)*(y+4)  under the condition  x*y = 80.  (1)

where x and y are the dimensions of the printed area.


In other words, from (1), you need to minimize

    f(x,y) = xy + 4x + 6y + 24 = 80 + 4x + 6y + 24 = 4x + 6y + 104.


From (1), you have  y = , so the function f(x,y) takes the form

    g(x) = 4x +  + 104 = 4x +  + 104.    (2)


So, you differentiate (2), and you get

    g'(x) = 4 - .


Equate it to zero

    g'(x) = 0 = 4 - .


So, to find x, you have this equation

     = 480,

     =  = 120

     x =  = 10.95 centimeters.


Then y =  =  = 7.30 cm.


Thus the dimension of the printed area are  10.95 cm width and 7.30 cm height.


The dimensions of the page are then  10.95 + 6 = 16.95 width and  7.30 + 4 = 11.30 cm height.