2.) As they age, honeybees move up in caste. Each week, 100% of eggs hatch into maids, 90% of maids mature into nurses and 10% of maids mature into workers. Each week, 70% of nurses mature into workers and 30% mature into foragers. Each week, 40% of workers mature into foragers. The queen lays eggs each week equal to 110% the current number of foragers. Initially, there are 200 eggs, 100 maids, 50 nurses, 25 workers, and 12 foragers.
a. Create a Markov model to represent the beehive. Included an initial state vector.
b. If each and every bee eats 1g of honey per week and each forager brings in 100g of honey per week, how much honey is made between now and 2 weeks from now?
c. What is the steady state of the system? Interpret this result in terms of the problem.
