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?

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

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:

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!

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

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

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

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!