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Lagrangian function and the kuhn-tucker conditions

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For each of the following functions, write the Lagrangian function and the Kuhn-Tucker conditions (including writing out the derivatives). You do not need to solve for the critical values. For all parts of this problem, x and y cannot be negative.
1. Maximize z = 3xy, subject to 2x + 2y ≤ 20
2. Maximize z = x2 + 2xy + y2, subject to 2x + y ≤ 24 and x + 3y ≥ 8
3. Minimize z = x2 + 2y2, subject to 4x - 3y ≥ 20 and 3x2 - 2y ≤ 15

Reference no: EM132669235

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