I don't understand what the Question is asking me

Question

The following polygon of constraints represents the solution for an optimization situation that involves minimizing the costs of sugar and salt. the values in the table below were calculated in order to determine the minimum cost. In this situation, how many solutions minimize the cost?

The table says

vertex A costs $50

vertex B costs $50

vertex C costs $75

vertex D costs $85

possible answers are greater than 3, greater than 2, greater than 1, and less than 2.

The polygon of constraints doesn't have any numbers on it so I don't know what I'm supposed to do with it and the question doesn't seem to make any sense either. I just can't figure out what the answer is.

Answer 1

In cost minimization (or profit maximization) problems, the reason we can generally look only at the vertices is the assumption that the cost/profit changes linearly along the borders between vertices.  That said, if A and B both have the same cost, what does that tell you about costs at all the points along the line between A and B?  

 

Hopefully that's enough of a hint to give you the answer.  If not, let me know.