Consider the Following Objective Function and Constraint: C(x) = 2x12

Multiple Choice

Consider the following objective function and constraint: C(x) = 2x12 - 15x + 3x23 - 9x2 + 30, such that x1 = 3x2. Which of the following is the correct Lagrangian function?

A) L = 2x₁² - 15x + 3x₂3 - 9x₂ + 30 - ? (3x₂ - x1)
B) L = 2x₁² - 15x + 3x₂3 - 9x₂ + 30 - ? (x₂ - 3x1)
C) L = 2x₁² - 15x + 3x₂3 - 9x₂ + 30 - ? (3x₁ - x2)
D) L = 2x₁² - 15x + 3x₂3 - 9x₂ + 30 - ? (3x₂ - 3x₁)