How to answer this question?

Consider a couple ranking purchased goods and services 0 and home-produced goods and services D as follows: U = CD where D is produced via a decreasing returns-to-scale technology f(hD) = Jig (so D = WE), using as input time hp subtracted from market work h. Suppose further that the indi- viduals can allocate 100 hours per week to either market work or home production. (a) (1 point) What is the optimal allocation of time between market and home production when the wage is 10 euros per hour? (b) (1 point) Suppose that now the couple has a child and, given the extra value of the time spent with the child, the joint utility becomes U = 0132 At the same time, any hour spent away from the child involves a cost of 5 euros to be paid to a babysitter. How does this affect the allocation of time of the family? (c) (1 point) Would your answer differ if home production technologies improve, (e.g., as a result of the introduction of disposable diapers and microwaves ovens), so that household production become f (h D) = h?) (assuming that utility function stays the same as in the previous point)