# Linear Programming: Relationship of Slope to Solution

When you watch this video, you will see iso-profit lines with different slopes sweeping across the feasible region starting at the origin and going as far as they can before leaving the feasible region. The further from line moves from the origin, the larger the profit becomes.

Watch the video and pay careful attention to where the maximum value of the objective function occurs and the slope of the edges of the feasible region.

Here are some points that you should get from the video. These are narrated in the video, but you may not have the ability to listen to them.

• The value of the objective function increases as the iso-profit line moves through the feasible region.
• The last corner point reached before exiting the feasible region is where the maximum value occurs.
• The slope of the iso-profit line determines which corner point will be the last one reached.
• A special case is when the slope of the objective function is the same as the slope of one of the boundaries of the feasible region. In this case, that edge of the feasible region will be the maximum solution.