Applied microeconomics allocations

A. How much time should be spent studying for each class? That is, maximize GPA by determining E* and U* subject to the 12 hour study time constraint.

b. Did this allocation of study time maximize or minimize your GPA?

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...=k (1)
dL/dU = 2/3*1/2*2(2U)^(-1/2)-k = 0 or 2/[3(2U)^(1/2)]=k (2)
dL/dk = E+U-12 = 0 (3)
(1)/(2): (2U/E)^(1/2)=2 or 2U/E=4 or U=2E (4)
Substitute (4) into (3), we ...