Pareto Optimality of Endowments Consider a $2*2$ exchange economy where individual $1$ has an endowment $(4,5)$ and individual 2 has an endowment $(6,5)$. 
The utility functions of individuals are represented by $U({x}_i{y}_i)$=${x}_i{y}_i$ where $i$ refers to individual $1$ or $2$.
I know that the allocations which equate $MRS$ for both individuals would be the Pareto Optimal allocations. However, I seem to be very confused regarding the endowments. I cannot find an allocation that is Pareto Superior to the endowments. Also, the endowment (if it is, in fact, Pareto Optimal) does not satisfy the equality of $MRS$ condition. 
Is it the case that equality of $MRS$ is not a necessary condition for pareto optimality? I can think of examples, such as Lexicographic Preferences which yield Pareto Efficient points without the condition of ${MRS}_i=$${MRS}_j$.
I think I'm missing out on something. 
My concepts seem quite shaky so please bear with me.
Given the endowments
Individual 1 : $(4,5); U(4,5) = 20$ and Individual 2 : $(6,5); U(6,5)=30$

Given that there is no more than and 10 units of Good X and 10 units of Good Y in the economy. If I allocate Individual 1 one with $X$ units of Good X and $Y$ units of Good Y then Individual 2 has $(10-X)$ units of Good X ($10-Y$) units of Good Y.

Now the set of Pareto superior allocations to the given endowments, if they exist will satisfy these two simultaneous non linear inequalities.

$ XY \geq 20$ Red region

$ (10-X)(10-Y) \geq 30$ Blue region

Graphically plotting these inequalities we observe: The small common region which you see between red and blue areas is actually the infinite set of all Pareto superior allocations to the given endowment.

Now our job is to find out that allocation which is Pareto optimal, that is that convex lens shaped common region should not be present.

This point could be achieved where both curves are tangent to each other.



Which are required Pareto optimal efficient/superior allocations.