1. (a) Define the slack and surplus variables. What do they represent? What is (are) the difference(s) between a slack and a surplus variable?

(b) Briefly describe the important parts of each step needed to make a decision using decision sciences models.

(c) What are the different types of special situations that may occur while solving a linear programming problem? Briefly describe each of these special situations.

(d) What are the important properties of a straight line? Briefly describe each property. What are the different types of slopes possible for a straight line? Briefly describe each type of slope and give one example for each type.

2. Determine whether the following linear programming problem is infeasible, unbounded, or has multiple optimal solutions. Draw a graph to find the feasible region (if it exists) and explain your conclusion.

Maximize 22xl + 32x2
Subject to:
2xl + x2 < 15
xl > 10
x2 < 10
xl, x2 > 0