Chapter3 Flashcards
1
Q
Front
A
Back
2
Q
What is the feasible region in a Linear Program (LP)?
A
- The feasible region is the set of all points that satisfy the constraints.
- It is convex.
- Can be bounded or unbounded.
3
Q
Where is the optimal solution in a convex feasible region?
A
- The optimal solution lies at an extreme point (vertex) of the convex region.
4
Q
What is an unbounded polyhedron?
A
- A feasible region where the objective value can increase infinitely in a particular direction.
5
Q
What happens if a linear program has no feasible solution?
A
- The problem is infeasible and the feasible region is empty.
6
Q
How do you transform a linear inequality to an equality?
A
- By adding a slack variable (e.g., for (x_1 + 4x_2 \leq 40), add (y_1) such that (y_1 + x_1 + 4x_2 = 40).
7
Q
What is the tableau form of a linear program?
A
- A system of equations organized in a matrix with the right-hand side.
- Used in the simplex method.
8
Q
What is a basic solution?
A
- A solution obtained by setting non-basic variables to zero.
- Corresponds to extreme points of the feasible region.
9
Q
What is the simplex method?
A
- An algorithm that moves from one basic solution to an adjacent one to improve the objective value.
10
Q
What is the pivot element in the simplex method?
A
- The pivot element is used to transform the tableau.
- It is found using the quotient rule and helps determine the entering and leaving variables.
11
Q
What is the termination criterion in the simplex method?
A
- When no negative coefficient remains in the objective row, the optimal solution is found.
