Final answer:
Building a private automated warehouse has the highest fixed costs due to expensive capital investments like land, construction, and automation technology.
Step-by-step explanation:
Among the options provided, building a private automated warehouse is likely to have the greatest fixed cost for a company. This is because constructing such a warehouse involves significant upfront capital expenditure on aspects like land acquisition, construction costs, and advanced technology for automation. These are all examples of fixed costs, which are expenses that do not change with the level of output or sales and are incurred regardless of business activity levels. In contrast, options such as leasing a warehouse or engaging in long-term public or contract warehousing entail lower upfront costs and thus generally have lower fixed costs compared to the building of an automated warehouse. Building a private warehouse to support manual operations would also involve lower fixed costs than an automated one, as the technology and machinery costs would be lower.