Consider two interconnected tanks similar to those in

Chapter 7, Problem 23

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Consider two interconnected tanks similar to those in Figure 7.1.6. Initially,Tank 1 contains60 gal of water and Q01 oz of salt, and Tank 2 contains 100 gal of water and Q02 oz of salt.Water containing q1 oz/gal of salt flows into Tank 1 at a rate of 3 gal/min. The mixturein Tank 1 flows out at a rate of 4 gal/min, of which half flows into Tank 2, while theremainder leaves the system.Water containing q2 oz/gal of salt also flows into Tank 2 fromthe outside at the rate of 1 gal/min. The mixture in Tank 2 leaves it at a rate of 3 gal/min, ofwhich some flows back into Tank 1 at a rate of 1 gal/min, while the rest leaves the system.(a) Draw a diagram that depicts the flow process described above. Let Q1(t) and Q2(t),respectively, be the amount of salt in each tank at time t.Write down differential equationsand initial conditions for Q1 and Q2 that model the flow process.(b) Find the equilibrium values QE1 and QE2 in terms of the concentrations q1 and q2.(c) Is it possible (by adjusting q1 and q2) to obtain QE1 = 60 and QE2 = 50 as an equilibriumstate?(d) Describe which equilibrium states are possible for this system for various values of q1and q2.