u (e) Set up a maximization problem for this household, where they maximize household's utility, subject to the family's budget constraint, and time constraints, by choosing how to allocate in, it\1. Consider a household utility U = tn(X :1, where X is nal goods from home production that directly affect the utility. And for X to he produced, Y has to be used. Let th, tw be the time spent by husband and wife in the production of X, And X = Y\" [mnm tw})1_" be the production function for nal home production good X. And hh, and hm be the hours the}.r spend in labor market, earning ton, and mm