Problem:
Consider the following, and answer problems:
Brian is taking three courses in this semester: economics, statistics, as well as finance. He has decided to spend 19 hours per week studying (in addition to attending all his classes) and his aim is to maximize his average grade, which means maximizing total of his grades in three courses. The table which are shows Brian's estimate of relation between time spend studying and his grade for each course. Notice it is assumed that Brian will spend at least four hours per week studying each of three courses.
|
|
Grade in
|
Grade in
|
Grade in
|
|
Hours of Study
|
Economics
|
Statistics
|
Finance
|
|
4
|
68
|
63
|
64
|
|
5
|
76
|
72
|
71
|
|
6
|
83
|
80
|
77
|
|
7
|
87
|
85
|
83
|
|
8
|
90
|
88
|
87
|
|
9
|
92
|
90
|
90
|
|
10
|
94
|
91
|
92
|
|
11
|
95
|
92
|
94
|
|
12
|
96
|
93
|
95
|
|
13
|
96
|
94
|
95
|
a. Is this the constrained optimization problem or unconstrained optimization problem?
b. If Brian is going to use a total of 19 hours the week studying what is optimal mix of studying between the 3 courses? That is, how many hours will he devote to economics? To statistics? To finance?
c. What is maximum average grade Brian can earn if he studies 19 hours per week?
d. What if Brian chooses to spend 25 hours, more willingly than 19, studying? How does the optimal mix change? How does maximum average grade change?