Question 4 (20 Points): Two tanks, each holding 1 L of liquid,are connected by a pipe through which liquid flows from tank A intotank B at a rate of (3 − a) L/min (0 < a < 3). The liquid insideeach tank is kept well stirred. Pure water flows into tank A at arate of 3L/min. Solution flows out of tank A at a L/min and outof tank B at (3 − a) L/min. If, initially, tank B contains no salt(only water) and tank A contains 0.1 kg of salt, answer the followingquestions: (a) Write the initial value problem corresponding to the problem described above in the form \mathbf{x}^{\prime}(t)=\mathbf{A x}(t), \quad \mathbf{x}(0)=\left[\begin{array}{l}

x_{1}(0) \\

x_{2}(0)

\end{array}\right] (b) Determine the mass of salt in each tank at time t ≥ 0, by solving the homogeneous system on item (a). (c) How does the mass of salt in tank A depend on the choice ofa? (d) Show that the time the tank B reaches its maximum amount of salt is given by t^{*}=\ln \left(\frac{3}{3-\alpha}\right)^{\frac{1}{\alpha}}