Researchers have reported the following data for the free radical copolymerization of methacrylonitrile (MAN) and alpha-methyl styrene (AMS) at 60 C. The collected data (roughly 6 weeks per collected point) consist of the mole fraction of MAN in the feed (xi) and mole fraction of MAN in the copolymer (yi). i Vi Xi 1 |0.2694 0.2145 2 0.5408 0.6074 3 0.6871 0.7831 4 0.7924 0.8976 A popular mechanistic model which can be used to describe binary copolymerizations is given by the following equation: nor + x(1- x;) Vi = - mix + 2x; (1 - x) + r,(1 - x. )2+ The symbols n and r2 are related to the relative reactivities of MAN and AMS (important parameters) to be estimated based on copolymerization data (as per table above). (a) (10 pts) Using n = 0.4 and 12 = 0.6 as initial values (guesses), determine point estimates for n and ry by the Gauss-Newton method, continuing the process until approximately 5 iterations. Show (or plot) the parameter estimates and the value of the objective function being minimized at each iteration step. (b) (10 pts) Using the point estimates from part (a), at what value of x should the next experimental run be carried out