An architect plans to outline a rectangular region with a fence and some shrubs. The fence costs 10 dollars per foot and will be placed along the north side as shown. The shrubs cost 25 dollars per foot and will be placed along the other three sides as shown. shrubs (a) Write a formula for the total cost of the fence and shrubs in terms of x and y. C = (in dollars) (b) If the rectangular region has an area of 200 square feet, express the total cost of the fence and shrubs in terms of x only. C(x) = (in dollars)

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) ).