Possibility curves

In the country of Rotorooa there are two regions, A and B. Two goods (x and y) are produced in both regions. Production functions for region A are given by

here l_x and l_y are the quantities of labour devoted to x and y production, respectively. Total labour available in region A is 100 units; that is,

Using a similar notation for region B, production functions are given by

There are also 100 units of labour available in region B:

a. Calculate the production possibility curves for regions A and B.

b. What condition must hold if production in Rotorooa is to be allocated efficiently between regions A and B (assuming labour cannot move from one region to the other)?

c. Calculate the production possibility curve for Rotorooa (again assuming labour is immobile between regions). How much total y can Rotorooa produce if total x output is 12? Hint: A graphical analysis may be of some help here.