To build a big line of exclusive products on its site, Amazon.com Inc. is pushing other brand manufacturers to do most of the work. The online retail giant is asking consumer-goods companies to create brands exclusively for Amazon after finding that developing them on its own is too costly and time-consuming, according to people familiar with the strategy. Equal sweeteners and nutrition brand GNC are among the first to launch products through an accelerator program Amazon launched last year to outsource the work. Mattress maker Tuft & Needle also recently created a new brand called Nod exclusively for Amazon. Amazon’s...