$(20$ points$)$ Please refer to the below diagram that accompanies the problem description.

I am feeding a mixture of two components, A and $B,$ to a separator. A is a very valuable

product, and the separation is designed to recover it from the feed stream. In order for

the process to be economical, I can tolerate no more than $25\%$ losses of A between the

feed and the Process Output, i$.$e$.,$ the Feed contains $125\%$ of the A that is found in the

Process Output. This separation leaves a Waste stream exiting the separator, which is $30$

$\%$ component A on a molar basis. However, recovering such a high percentage of the A

component comes at a pretty steep cost; the total flow rate of the process output is just

$60\%$ of the Feed stream. Find the composition of the Feed and the Process Output; report

your answer in either molar fractions or molar percentages.