It would be imperative to know what are the properties of LP and they are:
1) Proportionality
2) Additivity
3) Certainty
The main question which is important to understand is the feasible space which if known can enhance you search procedure to find the optimal point in the most efficient way. This feasible region/space (ABCDE, Figire 12.1) may of different types some of which are shown through case 12.1, case 12.2 and case 12.3. For this one can refer to Figure 12.2.
Case: 12.1

Case: 12.2
Case: 12.3

Figure 12.2: Different examples of feasible region/space |