Consider the two countercurrent heat exchanger designs for heating a cold stream from $t_{in}$ to $t_{out}$ as shown in figure. The hot process stream is available at $T_{in}$. The inlet stream conditions and overall heat transfer coefficients are identical in both the designs. The heat transfer area in Design $I$ and Design $II$ are respectively $A_{HX}^{I}$ and $A_{HX}^{II}$

If heat losses are neglected, and if both the designs are feasible, which of the following statements holds true:

1. $A_{HX}^{I}> A_{HX}^{II}\:\:\:\:T_{out}^{I}< T_{out}^{II}$
2. $A_{HX}^{I}= A_{HX}^{II}\:\:\:\:T_{out}^{I}=T_{out}^{II}$
3. $A_{HX}^{I}< A_{HX}^{II}\:\:\:\:T_{out}^{I}> T_{out}^{II}$
4. $A_{HX}^{I}< A_{HX}^{II}\:\:\:\:T_{out}^{I}= T_{out}^{II}$