Liann works in the olde tyme soda shopee. the shop sells milkshakes, double milkshakes, and triple milkshakes. a shake uses 1/8 cup of syrup, a double shake uses 1/4 cup of syrup, and a triple shake uses 3/ 8 cup of syrup. how many shakes of each kind could she make with 3 cups of syrup?

Consider the linear model for a two-stage nested design with b nested in a as given below. yijk=\small \mu + \small \taui + \small \betaj(i) + \small \varepsilon(ij)k , for i=1,; j= ; k=1, assumption: \small \varepsilon(ij)k ~ iid n (0, \small \sigma2) ; \small \taui ~ iid n(0, \small \sigmat2 ); \tiny \sum_{j=1}^{b} \small \betaj(i) =0; \small \varepsilon(ij)k and \small \taui are independent. using only the given information, derive the least square estimator of \small \betaj(i) using the appropriate constraints (sum to zero constraints) and derive e(msb(a) ).