A couple has 10 hours each that they can devote to housekeeping activities (H) and for childcare (C). The wife can provide 3 units of housekeeping or 1units of childcare in an hour; while the husband can provide 4 units of housekeeping or 2 unit of childcare in an hour.

1. If the plan is to have 12 units of housekeeping what is the maximum amount of childcare they can provide? Explain your answer by referring to the relevant concepts, and indicate the necessary division of work between the husband and the wife to achieve this maximum amount.

2. Suppose that for a happy child both the units of housekeeping (a clean house) and the units of care the child gets is important. But one unit of childcare makes the child 5 times happier as one unit of housekeeping. What is the productively and allocatively efficient production plan for the happiest child then? Who will do what? Explain by referring to what production and allocative efficiencies refer to.