
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Svetlana is certain that any feline can be interesting to her for two purposes - catching mice and conducting cat therapy. Based on these considerations, Svetlana decided to buy 2 kittens, each of which with equal probability can turn out to be either a male or a female. The weekly production possibility frontier (PPF) for males is given by $\mathrm{M}=80-4 \mathrm{~K}$, 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 dedicated to cat therapy.

(a) Determine the maximum number of mice that could be caught by 2 kittens per week with an optimal combination of males and females for this purpose.

(b) Determine how many different versions of the joint production possibility frontier Svetlana can have when acquiring 2 kittens.

(c) Determine the analytical and graphical form of the joint production possibility frontier for each of the possible combinations of males and females.

(d) As a result, the kitten seller delivered an order consisting of a male and a female, but also mentioned that the male has a twin brother whom Svetlana can accept for free. Determine the analytical and graphical form of the joint production possibility frontier if Svetlana agrees to accept the third kitten.

Present the answer in LaTex format: \boxed{Your answer}
user