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4. A stirred-tank blending system with a bypass stream is shown in Figure. The control objective is to control the composition of a key component in the exit stream, x4. The chief disturbance variables are the mass fractions of the key component in the inlet streams, x1 and x2. (1-1)Fi F1, X1 V (f)F1 F2, X2 F3, X3 F4, X4 Fi and xi represent the flow rate of stream i, and composition of key component in stream Fi, f is the bypass fraction. Assumptions i. The tank is perfectly mixed. ii. iii. Constant physical properties can be assumed because the composition changes are quite small. The bypass piping results in a negligible time delay. a. Write the model equations. b. Perform degrees of freedom analysis. c. Find the number of controlled and manipulated variables. d. Draw the control loops.