A Recap

Absolute Optimization 1.The domain is constrained to a closed and bounded region most of the time. 2.Closed and bounded regions are guaranteed to have absolute extremes. 3.We analyze the partial derivatives for extremes in the region only. 4.We analyze all paths. 5.We analyze all corner points. 6.We evaluate everything we found. The max is the highest z-value;The max is the highest z-value; The min is the lowest.The min is the lowest. Discard anything in between.Discard anything in between.

Find the first partials. Solve the system.. Keep all points in or on the feasibility region. Discard points outside the feasibility region.

Analyze each edge of the rectangle for any extremes between the end points (corners). No extremes here! Keep all points in or on the feasibility region. Discard points outside the feasibility region.

1.Evaluate every critical point and corner points. 2.The absolute maximum is the highest z- value. 3.The absolute minimum is the lowest z- value.

Actually there are two new constraints. They are parallel lines. They eliminate the origin from consideration and replace it with two new corner points.

This one slices the region into upper left and lower right. We need to make sure we choose the right region!

Suppose we had two machines (x and y). The value of each machine is $1,000 per unit of machine x use and $3,000 units of machine y use. We have set a limit of machine use for x and y of 4,000 units each. Similar we insist that use machine x and 2 y must be at least 1,000 units and no more than 9,000 units. Last we want the ratio of machine y to machine x to be 2 to 1. Read through the constraints carefully and you will see that except for scale (x and y in thousands of units)they do create our linear optimization problem.

Reread your on-line lessons.