During the season for harvesting wheat in the Free State, most farmers bring their deliveries of wheat to a central storage garner within a 2-week period, resulting in long waiting times for unloading and returning to the fields. To improve the efficiency of the unloading process, the storage garner is owned collectively by an association of wheat farmers in the Free State, and it is in every farmer's interest to mitigate costs due to grain deterioration, renting of delivery trucks, and idle driver time. Although crop damage is hard to ascertain, waiting and unloading costs of R18 per hour can be assigned to each truck and driver. The storage garner is open and operates 16 hours per day, 7 days per week, during harvest season and can unload up to 35 trucks per hour, following an exponential distribution. Full trucks arrive throughout the day, at a rate of around 30 per hour(following a Poisson pattern). To assist the farmersassociation, tackle the issue of lost time due to truck waiting and unloading, further analysis is needed by calculating the following:

(a) average number of trucks in the unloading system.[5]

(b) average time per truck in the system.[3]

(c) utilization rate for the bin area.[3]

(d) probability that there are more than three trucks in the system at any given time. [3]

(e) total daily cost to the farmers of having their trucks tied up in the unloading process. [6]

(f) The association mentioned earlier only utilizes the storage bin for two weeks per year. Farmers estimate that expanding the bin would result in a 50% reduction in unloading costs next year. However, this would require an offseason investment of R9,000. Determine if it is worthwhile for the cooperative to enlarge the storage area, a cost-benefit analysis is necessary.[5]