Task $1(15$ marks$)$

ABG industries manufactures engine, transmission, and chassis parts for manufacturers and repair companies in the United States, South America, Canada, Mexico, Asia, and Europe. The company transports parts to its foreign markets by container ships. To serve its customers in South America and Asia, ABG has large warehouse and distribution centres. In Europe, it ships into Hamburg and Gdansk, where it has contracted with independent distribution companies to deliver its products to customers throughout Europe. However, ABG has been displeased with a recent history of late deliveries and rough handling of its products. For a time ABG was not overly concerned because its European market wasn't too big, and its European customers didn't complain. Plus, it had more pressing problems elsewhere. However, in the last few years, trade barriers have fallen in Europe, and Eastern European markets have opened up$.$ ABG's European business has expanded, as has new competition, and its customers have become more demanding and quality conscious. As a result, ABG has initiated the selection process for the site of a new European warehouse and distribution centre. Although it provides parts to a number of smaller truck and auto maintenance and service centres in Europe, it has seven major customers$-$ auto and truck manufacturers in Vienna, Leipzig, Budapest, Prague, Krakow, Munich, and Frankfurt. Its customers have adopted manufacturing processes requiring continuous replenishment of parts and materials.

ABG's European headquarters is in Hamburg. The vice president for construction and development in Dayton, Ohio, has asked the Hamburg office to do a preliminary site search based on proximity to customers and mileage. Each container is converted to a single tractor$-$trailer truckload. The number of containers shipped annually to each customer is as follows: Vienna, $150$; Leipzig, $110$; Budapest, $175$; Prague, $215$; Krakow, $95$; Munich, $130$; and Frankfurt, $60.$ When the vice president of construction in Dayton received this information, he pulled out his map of Europe and began to look for possible sites.

Recommend a city site for the European warehouse and distribution centre that minimises the total annual delivery mileage. Please show all the steps and workings in arriving at the decision. $($All steps and workings should be indicated on the sheet$]$