Use MATLAB for the following simulations scenario:

Owner of a car park with n parking places plans to expand the parking area with n new parking places.

The owner has kept a record of the parking times for two years and also monitored the interarrival times of cars that came into the parking area to check if there are free parking places.

Thus, the probability density distributions t_park p_t() for the parking times (in minutes) and t_interarrival pi() for the inter-arrival times (in minutes) of incoming cars are known.

The parking fee is c euros / min for cars that use parking place. The cost of building a new parking place is d euros / parking place.

The goal of the owner is to maximize the profit gained in T years period by choosing an optimal number of parking places in the parking area. (You can assume zero discount rate.)

Consider solving this problem with direct simulations of the daily income and costs of the parking place. Give a rough pseudo-algorithm of a direct simulation that can be used to make the decision of the optimal number of new parking places assuming that

a) 5p if there is no free parking place, the cars wait in a queue until they find a free place.

b) 2p if there is no free parking place, the car drives away without paying any fee.