Maynard is the owner of a small car-rental company with a fleet of 4 cars which he rents on a daily basis at $5000 per day. Records show that the daily demand for cars can be modelled by a Poisson distribution with mean 4.

(a) Calculate the probability that all requests for cars can be be met on one particular day.

(b) Calculate the expected daily income received from rentals.

(c) It is expected that the cost of increasing  by one car is $2500 per day. Determine whether the company can expect to increase its profits by doing t