Question

You are taking two courses this semester: biology and chemistry. You have two examinations coming up in both classes. The table below shows your grade on each examination for different numbers of hours spent studying for each: Hours of Study Mathematics Economics 0 70 77 82 60 1 68 2 74 3 85 78 Your goal is to maximize your average grade on the two quizzes. Use the idea of optimization in differences to decide how much time you would spend studying for each quiz if you had three hours in total to prepare for the two exams. Note: you can only choose to study in increments of one hour

Answer 1

For deciding which subject to study we must see in which subject the marginal increase in marks is more.

We have a total of 3 hours time

Lets check

For First hour of study :-

Marginal Increase in marks in Economics for its first hour = 77 - 70 = 7

Marginal Increase in marks in Maths for its first hour = 68 - 60 = 8

As 7 < 8 so we will give the first hour to Maths.

For Second hour of study :

Marginal Increase in marks of Economics for its first hour = 77 - 70 = 7

Marginal increase in marks of Maths for its Second hour = 74 - 68 = 6

As 7 > 6 so we will give the second hour on Economics.

For the third hour of study :

Marginal increase in marks of Economics for its second hour = 82 - 77 = 5

Marginal increase in marks of Maths for its second hour = 74 - 68 = 6

As 5 < 6 so we will give the third to Maths.

Hence,

We gave the First and the third hour on Maths and the second hour on Economics

So, We will give 2 hours on Maths and 1 hour on Economics of we had total time of 3 hours