A student wishes to minimize the time required to gain a given expected average grade, m, in her end-of-semester examinations. Let ti be the time spent studying subject i ∈ {1,2}.

Suppose that the expected grade functions are g₁(t₁) = 40+8√t1 and g₂(t₂) = 2t₂.

Thus the individual's optimization problems is to choose t1 and t2 to minimize total studying time T = t₁ + t₂ subject to obtaining a mean grade of m where m - [g₁(t₁)+g₂(t₂)]/2 = 0

• I need to write down the Lagrangian for the individual's optimization problem and solve for the optimal choices of t1, t2 and T in the case where the student wishes to obtain an expected mean grade of 70. So I think:

Min T(ti, t2) = t1 + t2

S.t. 20 + 4√t1 + t2 - m = 0

• Check the second order conditions
• How can the LM, λ*, be interpreted in this case?

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