0006. It's the end of the semester and it's time to optimize. I have a sociology final exam and a public policy final exam on the same day and I can only allocate 16 hours total to exam preparation.
I estimate that if I do not study at all, I'll get C- in public policy and a C+ in sociology. But, experience has shown that studying pays off. In sociology, each hour of study raises my grade by 1/3 (0.33) of a letter grade (C- to C, for example). In public policy, the payoffs are not as quick: each 2 hours yields 1/3 of a letter grade (0.167 grade per hour).
Thus, 3 hours of sociology study would take me from C+ to B+

 C 1 hour > B- 1 hour > B 1 hour > B+

Our plans are subject to a number of constraints:

• There is a four hour public policy study session planned with the professor and it would be unwise and impolitic not to attend. Thus, PPOL hours has to be at least 4.
• Since the top grade is A, sociology will top out at 5 study hours since these will take me from C+…B-…B…B+…A-…A and in public policy my max is correspondingly 14 with each 2 hours taking me one grade of the seven steps from C- to A.
• Total study hours must be 16 or less.
• Since I am a public policy major, I feel strongly that I have to study more for PPOL than for SOCIOLOGY

I translate these into five inequalities

• (Only 16 hours ) PPOL = -SOC + 16
• (More PPOL than SOCIOLOGY) PPOL ≥ SOC
• (PPOL Study Group) PPOL ≥ 4
• (SOCIOLOGY max) SOC ≤ 5
• (PPOL max) PPOL ≤ 14

I want to know how to divide my study time so as to maximize my grades. Let's start with a typical Excel layout for a simple LP problem.

Identify the lines in this chart, indicate the feasible set, and find the optimal value of the variables and the resulting value of the objective function.

page revision: 16, last edited: 13 Dec 2011 19:29