Suppose you have two exams, Mathematical Economics (M) and Statistics (S). You h

Question

Suppose you have two exams, Mathematical Economics (M) and Statistics (S). You have 12 hours each day in which to study for the two exams. You figured out that your GPA, for you two courses takes the form:

GPA=2/3[squarerootM +squareroot(2S)]

Where M is the number of hours per day spent studying for Mathematical Economics and S is the number of hours per day spent studying for Statistics.

(a) What is the optimal number of hours per day spent studying for each course?

(b) if you follow this strategy what will be your GPA?

Explanation / Answer

a)GPA=2/3(M0.5+(2S)0.5)

M+S=12 this gives,M=12-S

GPA=2/3((12-S)0.5+(2S)0.5)

Differentiating dGPA/dS

2/3(-1/2(12-S)-1/2+(2S)-1/2)=0

this gives S=8

Hence For Maximum GPA S=8,M=12-8=4

b) GPA at S=8,M=4

2/3(41/2+(2*8)1/2)=2/3(2+4)=4

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