What is the maximum value of $\frac{7x+2y}{2x+2}+\frac{3x+8y}{2y+2}$ while $0≤x,y≤1$ 
Find  maximum value of $\left(\dfrac{7x+2y}{2x+2}+\dfrac{3x+8y}{2y+2}\right)$ for $0≤x,y≤1$

My approach was to use A.M-G.M inequality or cauchy shbert inequality, but I failed.

$$
f(x,y) = \frac{7x+2y}{2x+2} + \frac{3x+8y}{2y+2} 
= 
\left( \frac 72 - \frac{7-2y}{2x+2} \right)+ 
\left( 4 - \frac{8 - 3x}{2y+2} \right)
$$
is strictly increasing in both variables on $[0, 1]^2$, therefore
$$
 f(x, y) \le f(1,1) = 5
$$
with equality exactly for $(x, y) = (1,1)$.
