A multi$-$unit process in a chemical$/$biomedical plant operates as shown in the flowchart below with the tank volumes $($gallons$),$ brine flow rates $($gal$/$min$)$ and initial salt contents $($Ib$)$ as indicated to maintain the volume in each tank steady$/$constant$.$ Construct a mathematical model $($i$.$e$.,$ derive the fundamental design equations$)$ for the system of ODEs that would need to be solved to obtain the number of pounds of salt $y_1(t),y_2(t),y_3(t),$ and $y_4(t)$ at any time $t$ in tanks $T_1,T_2,T_3,$ and $T_4$ respectively. Write your final answer in matrix form $(($:$y^{\text{'}}=Ay\}.$ Without solving the system of equations, predict the limiting values of $y_1(t),y_2(t),y_3(t),$ and $y_4(t)$ as $t.$