For the liquid storage system shown in Fig. E, it is desired to control liquid levels h1 and h2 by adjusting volumetric flow rates q1 and q2. Flow rate q6 is the major disturbance variable. The flow-bead relations arc given by where Cv1, Cv2, and K are constants.(a) Derive an expression for the relative gain array for this system.(b) Use the RGA to determine the recommended pairing of controlled and manipulated variables for the following conditions:Parameter ValuesNominal Steady-StateValues

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- Caha a- Kh - h) K-3 gailnin it C- 3 gal/min fs D - D2 - 15 t (tack diameters) LT