Solve the following constrained optimization problems, where possible. a. Maximize x + 2y such that x +

Solve the following constrained optimization problems, where possible.

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a. Maximize x² + 2y² such that x² + y² = 4. b. Minimize x + 2y² such that x + y² = 1. c. Minimize 2x² + y² - ² such that 3xy - 42² = 0. d. Maximize -y +z-x+6 such that x - y-z = 2 and x² + y² = 1.