1. An example of interactive technology
Interacting with a model to learn
about sensitivity analysis.
2. How would you tell someone
about sensitivity analysis in LP?
• The following (4 slides) illustrates how beginning LP students
can interact with a model to learn about sensitivity analysis.
They are guided thru an understanding of concepts by
visualization of the result of parameter changes as they
interact with the data set.
• While the idea of a solution to a LP problem is fairly easy to
understand, the sensitivity of the change of solution given a
change in a parameter is often a stumbling block for the
beginning student. It is often skipped by, and a sensitivity
range is given so that the application of it can proceed -- the
emphasis is often on the interpretation of the range. How the
range actually evolves is both interesting and fundamental to
a clear understanding of LP. In 2 variable LP we can see how
the ranges evolve, and then use this as a comfort in working
with LP problems in more than 2 variables.
3. We start with a simple model. The coefficients of the Z function and of the
constraints are entered, and the graph appears by clicking the graph button.
The Z function is 4*x1+5*x2, creating the dotted iso-profit line. The feasible region
for the model is the area simultaneously beneath the blue and red constraint lines.
4. The dotted iso-profit line is moved away from the origin and out of the feasible
region by incrementally clicking the increase button.
The iso-profit line leaves the region at the corner point (10,15),
marking it as optimal.
5. Now, the model is changed by altering the x1 coefficient of Z. The 4 is changed
to 2, representing that the profit from the 1st product is 2 instead of 4.
Hitting the graph button draws the new graph with new Z iso-profit line.
6. Moving the new iso-profit line thru the feasible region gives a new optimal point.
It’s (0,20). The student now realizes that if the iso-profit line
were steeper than the first constraint line, the change of optimality would not
occur until it was as steep or steeper than the second constraint line.
7. The Big Idea is that people learn from
doing the interaction, not just seeing it!
Download a copy of LPemli from
Do some interactions and see what I mean.
Use it for free, no strings attached, for learning
the basics of Linear Programing. 23 pages of
interactive, visual learning that’s easy on the
Requires Excel 2010 for the PC
Excel 2011 for the MAC