Problem 5: Optimization The last problem is intentionally vague (there are potentially many ways to answer the problem). I want to see how you think about formulating an optimization problem, given some (incomplete) information. A student wants to maximize their GPA for the semester. They are taking four courses: econ, math, comp, and poli-sci. They have a total of 560 hours in the semester to commit to study; time is continuous and takes values in [0, 560]. GPA is also a continuous variable, taking values in R+, and is determined by the amount of time the student spends working on each of the courses. There are increasing returns to time spent working on each of the courses: every additional hour (minute or second) spent working on a course increases overall GPA. There are decreasing marginal returns to time spent working on each of the courses: the first hour (minute or second) increases GPA more than the second hour (minute or second), the second hour (minute or second) spent working on a course increases overall GPA more than the third hour (minute or second), and so on. Econ and math are easy courses; comp and poli-sci are hard. An hour (minute or second) spent working on econ or math increases overall GPA twice as much as an hour spent working on comp or poli-sci. The student must attend lectures. For econ and math there are two lectures a week and a recitation. For comp and poli-sci there are two lectures (no recitations). Each lecture is one hour long, and each recitation is one hour long. There are 14 weeks. Propose a model to describe the problem facing this student. You should propose appropriate choice variables, parameters, an objective function, and constraint functions, so that you can formulate the student’s problem as an optimization problem. You do not need to solve the optimization problem, but you should justify the way that you have set the problem up.
Problem 5: Optimization
The last problem is intentionally vague (there are potentially many
ways to answer the problem). I want to see how you think about formulating an optimization problem, given some (incomplete) information.
A student wants to maximize their GPA for the semester. They are
taking four courses: econ, math, comp, and poli-sci. They have a total
of 560 hours in the semester to commit to study; time is continuous
and takes values in [0, 560]. GPA is also a continuous variable, taking
values in R+, and is determined by the amount of time the student
spends working on each of the courses.
There are increasing returns to time spent working on each of the
courses: every additional hour (minute or second) spent working on a
course increases overall GPA.
There are decreasing marginal returns to time spent working on each
of the courses: the first hour (minute or second) increases GPA more
than the second hour (minute or second), the second hour (minute or
second) spent working on a course increases overall GPA more than
the third hour (minute or second), and so on.
Econ and math are easy courses; comp and poli-sci are hard. An hour
(minute or second) spent working on econ or math increases overall
GPA twice as much as an hour spent working on comp or poli-sci.
The student must attend lectures. For econ and math there are
two lectures a week and a recitation. For comp and poli-sci there are
two lectures (no recitations). Each lecture is one hour long, and each
recitation is one hour long. There are 14 weeks.
Propose a model to describe the problem facing this student. You
should propose appropriate choice variables, parameters, an objective
function, and constraint functions, so that you can formulate the student’s problem as an optimization problem. You do not need to solve
the optimization problem, but you should justify the way that you
have set the problem up.
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