# Problem 4. Maximum 20 points

Svetlana is convinced that any feline can be interesting to her for two purposes - catching mice and conducting cat therapy. Based on these considerations, Svetlana has decided to acquire 2 kittens, each of which has an equal probability of being either a male or a female. The weekly production possibility curve for males is $\mathrm{M}=80-4 \mathrm{~K}$, and for females $\mathrm{M}=16-0.25 \mathrm{~K}$, where $\mathrm{M}$ is the number of mice caught per week, and $\mathrm{K}$ is the number of hours devoted to cat therapy.

(a) Determine the maximum number of mice that 2 kittens can catch in a week with the optimal combination of males and females for this purpose.

(b) Determine the number of different variants of the combined production possibility curve Svetlana has when acquiring 2 kittens.

(c) Determine the analytical and graphical form of the combined production possibility curve for 2 kittens for each of the possible combinations of males and females.

(d) In the end, the kitten seller delivered the order, consisting of a male and a female, but also noted that the male has a twin brother, whom Svetlana can receive for free in her caring hands. Determine the analytical and graphical form of the combined production possibility curve if Svetlana agrees to the offer to take the third kitten.