1. Model #6 The Student’s Dilemma
Recapitulation of the problem
You need to pass both French and Calculus
You have $100 to spend on a calculus tutor ($15/hr) and in the language lab ($5/hr)
You cannot spend more than 11 hours on both language and math lessons
What is the optimum solution?

2. Model #6 The Student’s Dilemma
A solution path that most people chose
Let F equal the number of hours in the language lab and M the number of hours with the math tutor. Then:
Furthermore, the money factor can be written as

3. Model #6 The Student’s Dilemma
There are two more constraints
The maximum number of hours that can be spent in the language laboratory is:
The maximum number of hours to be spent with the math tutor is:

4. Model #6 The Student’s Dilemma
Most teams derived and solved these constraint “equations” to get
The time spent is exactly 11 hours and the money spent is exactly $100!

5. Model #6 The Student’s Dilemma
The constaint equations can also be displayed
graphically - with interesting results:
Solution Space

6. Model #6 The Student’s Dilemma
Suppose we added two more constraints - suppose we figure we must study calculus at least 3 hours and French 2 hours to pass. We can easily add this to graphical representation
Solution Space
now reduced

7. Model #6 The Student’s Dilemma
This graphical approach is part of a process known as optimization through linear programming
All feasible solutions are found inside the solution space - all solutions outside the solution space are infeasible
The “maximum” and the “minimum” solutions are found on the boundaries

8. Model #6 The Student’s Dilemma
With the graphical approach, you can examine quickly how the
solution space changes with alterations in the constraints. For
example, suppose you have more (or fewer) hours to study:
Note how optimum
solution changes -
different constraints
determine the final
solution!