Optimization techniques are used in many applications. For example, when customers order products from an online store, the shipper must determine the optimal way to get the product delivered to the customer. The delivery path that is chosen is the path that minimizes shipping costs while simultaneously satisfying these constraints:

1. The product must arrive by a promised date.
2. The shipper must deliver a finite set of items.
3. The product must originate from one of several warehouse hubs across the country.

Discuss whether there can be multiple solutions (i.e., more than one path to get the product to your house). Explain why. Is there a guarantee that a solution always exists? Explain.