Problem 13-19 John and Sons Wholesale Fruit Distributors employone worker whose job is to load fruit on outgoingcompany trucks. Trucks arrive at the loading gate atan average of 24 per day, or 3 per hour, according toa Poisson distribution. The worker loads them at arate of 4 per hour, following approximately the exponentialdistribution in service times.Determine the operating characteristics of this loading gate problem. What is the probability thatthere will be more than three trucks either being loaded or waiting? Discuss the results of your queuingmodel computation.

Problem 13-20 John believes that adding a second fruit loader willsubstantially improve the firm's efficiency. He estimates that a two-person crew, still acting like asingle-server system, at the loading gate will doublethe loading rate from 4 trucks per hour to 8 trucksper hour. Analyze the effect on the queue of such a change and compare the results with those found inProblem 13-19.

Problem 13-21 Truck drivers working for John and Sons (see Problems13-19 and 13-20) are paid a salary of $10 perhour on average. Fruit loaders receive about $6 perhour. Truck drivers waiting in the queue or at the loading gate are drawing a salary but are productivelyidle and unable to generate revenue during that time. What would be the hourly cost savings tothe firm associated with employing two loaders instead of one?

Problem 13-22 John and Sons Wholesale Fruit Distributors (ofProblem 13-19) are considering building a second platform or gate to speed the process of loading theirfruit trucks. This, they think, will be even more efficientthan simply hiring another loader to help outthe first platform (as in Problem 13-20).Assume that workers at each platform will beable to load 4 trucks per hour each and that truckswill continue to arrive at the rate of 3 per hour. Findthe waiting line's new operating conditions. Is thisnew approach indeed speedier than the other twoconsidered?