from gekko import GEKKO
m = GEKKO()
tabs = 5.0 / 100 # m = cm * (1m/100cm)
Area = 0.8       # m^2
w = m.Var(lb=0)    # width of the cardboard piece
x = m.Var(lb=0)    # length of cut-out
h = m.Intermediate(Area / w) # Area = w h
box_width  = m.Intermediate(w - 2 * x)
box_length = m.Intermediate(h - 2 * x)
box_height = m.Intermediate(x)
box_width_with_tabs = m.Intermediate(box_width + 2 * tabs)
Volume = m.Intermediate(box_width * box_length * box_height)
# upper constraint for box width with tabs
m.Equation(box_width_with_tabs < w)
# lower constraint for box width with tabs
m.Equations([box_width > 0,box_length > 0,Volume>0.01])
m.Maximize(Volume)
m.solve()
print('width = ' + str(w.value[0]))
print('length = ' + str(h.value[0]))
print('height = ' + str(x.value[0]))
print('volume = ' + str(Volume.value[0]))