Lupe Martinez started the Martinez Grocery Company after years of frustration in not being able to get good, fresh baked goods in San Francisco. Martinez Grocery originally specialized in cake, tarts, breads, and doughnuts sold from Lupe's home. Her success among the affluent, gourmet food crowd allowed her to expand to a second location within six months and to a half-dozen outlets within the first year. Due to customer requests, she expanded into bagels, ready-made salads, and other manufacturers' products such as gourmet ice cream and gourmet pet food. Once Lupe got beyond a dozen stores, the expense and administrative burden of overseeing all those kitchens caused Lupe to maintain a central kitchen/supply location downtown that restocked all the stores. Currently, the distribution center is causing problems in the form of underutilized employees and long lines for truck loading. The loading dock at the distribution center will accommodate only one truck for loading or unloading at a time. Company-owned trucks arrive according to a Poisson distribution with a mean rate of three trucks per day. At present the company employs a crew of three to load and unload the trucks, and the unloading/loading rate is Poisson distributed with a mean rate of five trucks per day. The company can employ additional (or fewer) persons in the loading crew and increase the average loading rate by one truck per day for each additional employee up to a maximum of six persons who can be utilized effectively in the process (for example, four workers could load/unload six per day, or two workers could load/unload four per day). The company estimates that the cost of an idle truck and driver is $80 per hour and the company pays $17 per hour (including benefits) for each employee in the loading crew. Loading dock crew members and truck drivers work eight hours per day. Lupe called in Joe Freeman, foreman of the loading crew, to her office to discuss the problem. Luke contends that they are overstaffed. He dislikes seeing idle workers, and is roundly feared by the loading crew. "We can be more profitable if we fire one of these so-called workers," Luke said. "They are always just sitting around waiting for trucks to come in." Luke's comments seemed true enough, but the trucking supervisor had recently told Lupe that the truckers' feelings were hurt by the long lines they had to sit in waiting to be unloaded.

1. Advise Lupe on the proper number of loading dock personnel to employ to minimize costs under the current system. Include the calculations you did to develop your recommendation.

2. Note any operational changes that could be made to improve the situation