The document discusses linear programming problems (LPP) and their graphical solution method. It defines LPP as problems that involve minimizing or maximizing an objective function subject to constraints. The graphical method finds the optimal solution by determining the point of intersection between the objective line and feasible region. Three examples of LPPs are given involving minimization with two constraints, maximization with three constraints, and three practice problems to solve using the graphical method.

1. Topic : Linear Programming Problem
Minimization with two constraints
Maximization with three constraints

2. Graphical Method of Linear Programming
Problem
Is used for solving the problems by finding out
the maximum or minimum point of the
intersection between the objective line and the
feasible region

3. Optimal Solution
is the maximum or minimum
value of an objective function for
the given problem.

4. Solve the following LPP using graphical
method
Minimize z= 4𝒙𝟏 +6𝒙𝟐
Subject to
𝒙𝟏 + 𝒙𝟐 ≥ 8 above the feasible region
6𝒙𝟏 + 𝒙𝟐 ≥12 above the feasible region
𝒙𝟏 and 𝒙𝟐 ≥ 0

5. Solve the following LPP using graphical
method
Maximize z= 100𝒙𝟏 +6𝟎𝒙𝟐
Subject to
5𝒙𝟏 + 𝟏𝟎𝒙𝟐 ≤ 50 below the feasible region
8𝒙𝟏 + 𝟐𝒙𝟐 ≥16 above the feasible region
3𝒙𝟏 - 𝟐𝒙𝟐 ≥6 above the feasible region
𝒙𝟏 and 𝒙𝟐 ≥ 0

6. Activity 1: Solve the following LPP using graphical
method.
1.Minimize z= 𝟖𝒙𝟏 +10𝒙𝟐
Subject to
𝒙𝟏 + 𝒙𝟐 ≥ 10
8𝒙𝟏 + 𝒙𝟐 ≥24
𝒙𝟏 and 𝒙𝟐 ≥ 0

7. Activity 1: Solve the following LPP using graphical method.
2. Minimize z= 𝟓𝒙𝟏 +10𝒙𝟐
Subject to
𝟐𝒙𝟏 + 𝒙𝟐 ≥ 10
𝒙𝟏 + 𝟕𝒙𝟐 ≥28
𝒙𝟏 and 𝒙𝟐 ≥ 0

8. Activity 1: Solve the following LPP using graphical method.
3. Maximize z= 80𝒙𝟏 +40𝒙𝟐
Subject to
6𝒙𝟏 + 𝟏𝟐𝒙𝟐 ≤ 60
4𝒙𝟏 + 𝟐𝒙𝟐 ≥12
3𝒙𝟏 - 𝟔𝒙𝟐 ≥12
𝒙𝟏 and 𝒙𝟐 ≥ 0