See worksheet $$Transportation $-$ Utility$,$ where we are solving a variation of the transportation

problem. Each customer has a utility function, and we want to maximize total customer utility subject to

the constraints that: $($i$)$ suppliers cannot exceed their capacity; and $($ii$)$ we cannot exceed our total budget

for variable shipping cost. Note that there is no demand constraint in this problem, the customer demand

is now expressed through their utility functions in the problem objective. We want to make the customers

collectively as happy as possible, subject to our supplier capacity constraints and variable shipping cost

constraints.