Vtyjkyuk

I have the following problem and I don't know which way to go. The problem is about building a card minimizing the amount of paper used subject to this:

1-The area must be 100cm**2
2-Upper edge is 2cm and lower one is 3cm
3-Righ and left edges are 5cm each

After making it abstract, I get the following, being x the vertical side, y the horizontal one, x0 the vertical side minus the edges, y0 the horizontal one minus the edges:

x•y = 100
x = x0 + 2 + 3, x = x0 + 5
y = y0 + 2•5, y = y0 + 10

which leads me to:

(x0 + 5)•(y0 + 10) = 100,
x0•y0 + 5y0 + 10x0 + 50 = 100
x0•y0 + 5y0 + 10x0 = 50

my problem comes after here, because if I want to use a single variable setting y0 after x0 i get this:

(x0 + 5)•y0 = 50 - 10x0,
y0 = 10•((5-2x0)/(x0 + 5)),
y0 = 10•((-2) + (15/(x0 + 5))),
f(x) = (-20) + (150/(x0 + 5))

then I want to optimize it, and I get

f'(x) = 0 - 150•(1/((x0+5)**2))

which, when equalled to 0 results wrong ly:

f'(x) = 0 = 150•(1/((x0+5)**2)),
0 = 1/((x0+5)**2),
0 = 1, which is impossible.

Therefore, I have to assume it's impossible to optimize.

Should I proceed using 2-variables optization or did I commit any procedure error? Thanks for your answers

Also, excuse my bad writting but I'm using the mobile app for the first time and I don't know how to set subindexes and such. Also, my language is a portmanteau of my maths knowledge, which is in Spanish, so I can't do much about it at the moment