The solution will always be on the edge of the feasible region. There may be a local optimum that is not the global optimum. All of these are true. Real world LP applications, unlike the simplified versions in the text, may a. not be concisely stated b. have a smaller number of variables and constraints c. involve data which is not readily available. If sensitivity analysis shows an allowable increase of infinity for the objective function coefficient range for variable x1, it means that a. the problem is unbounded.
Mathematics can only guarantee an optimal in terms of one performance measure.
Both linear and non-linear problems need constraints, to have a bounded optimal solution. The algorithm for non-linear optimization could find a local optimum that is not the overall global optimum. The course notes compared optimization to a function like the square root function. The reduced cost is a. the amount by which the objective function would change if the simple limit on the decision variable were increased by 1. The allowable increase and decrease for objective function coefficients a. is the range within which the shadow price stays the same.