The consumption of two types of manufacturing goods (X and Y) follows a hypothetical joint probability density function as follows:
fXY(x, y) = c(x^(1/2) + y2) for 0 < x < 1 and 0 < y < 1
where x and y are normalized to the respective maximum value for all the houses. Determine the constant c such that fxy(x,y) is a legitimate joint density function.