Suppose that a family's demand for milk depends on milk price :1: > 0 and the family's income 3; > 0 according to the function: day) = Ax'"yb (1} where A, a and b are positive constants. (a) Find a constant k (in terms of the constants a and 5} such that 62mm 32mm} _ ax +13; ay _ kz(x,y). (I? (b) Based on data for the period 1995 2005, it is estimated that milk demand could be repre- sented by equation (1} with o: = 1.5 and b = 2.1. Calculate the value of k in this case. (c) For the values of o; and 3; given in (b), assume that :r: = 3:03) 2 x0 x (1.06)' and y 2 y(t) 2 ya x (1.08)' in (1} are both functions oftime t, where 3:0 is the price and go is the income at timet = 0. Thus, z(:r(t),y(t)) = 2(t) is also a function of time 1%. Calculate the proportional rate of growth, which is dened as the derivative of In (2:08)) with respect to t