Please only do (v) through (vii) A certain college student is cramming for final

Question

Please only do (v) through (vii)

A certain college student is cramming for finals and has only six hours of study time remaining! Her goal is to get as high an average grade as possible over three subjects: economics, statistics, and mathematics. She must decide how to allocate her remaining study time among the subjects. Based on the best estimates she can make, her grade in each subject will depend on the time allocated studying it according to the following schedule: Economics Math Stats Hrs. Grade Hrs. Grade Hrs Grade 20 45 65 40 80 90 94 68 74 78 81 80 4 82 86 89 4 4 97 97

Explanation / Answer

THIS PROBLEM IS BASED ON THE LAW OF DIMINISHING MARGINAL UTILITY.

V. MARGINAL BENEFIT FOR FIRST TWO HOURS IS MOST IN CASE OF ECONOMICS, NEXT TWO HOURS WITH A HIGHER BENEFIT ARE IN MATH, GAIN NEXT ONE HOUR SHOULD BE GIVEN TO STATS AND THE REMAINING ONE HOUR SHOULD BE DEVOTED TO ECONOMICS AGAIN. SO HE SHOULD DEVOTE THREE HOURS TO ECONOMICS, TWO HOURS TO MATH AND ONE HOUR TO STATS.

CORRESPONDING VALUES AT ECONOMICS 3 ARE 77, MATH 2 ARE 68 AND STATS 1 ARE 90

AVERAGE = (77 + 68 + 90) / 3 = 235 / 3 = 78.33

VI. LARRY ADVICE IS TO GIVE ALL TIME TO STATS

SO AVERAGE WILL BE (96 + 20 + 40) / 3 = 156 / 3 = 52.

VII. MOE'S ADVICE IS TO GIVE ALL TIME TO ECONOMICS

SO AVERAGE WILL BE (89 + 40 + 80) / 3 = 209 / 3 = 69.67

VIII. STUDYING ECONOMICS DOES EXHIBIT DIMINISHING RETURNS BECAUSE SUCCESSIVE MARGINAL BENEFITS DO DECLINE.

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