I Consider the following function f = Mx + Mx - 4xx + 4x where f...

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I Consider the following function f = M²x² + Mx² - 4x₁x₂ + 4x₁ where f is the aircraft fuel burn (objective function), M is the Mach number, and x₁ and x₂ are the relative spans and chords of the wing (design variables), respectively. Conduct a multi-point optimization that can balance the fuel burn at Mach numbers 1 and 2. Note that the fuel burn at Mach numbers 1 and 2 are equally important. Requirements: a) Derive the multi-point optimization formulation, i.e., ƒ as a function of x₁ and x₂ (30%) b) Solve the multi-point optimization problem and report the optimal objective function f* and design variable x*. (70%) I Consider the following function f = M²x² + Mx² - 4x₁x₂ + 4x₁ where f is the aircraft fuel burn (objective function), M is the Mach number, and x₁ and x₂ are the relative spans and chords of the wing (design variables), respectively. Conduct a multi-point optimization that can balance the fuel burn at Mach numbers 1 and 2. Note that the fuel burn at Mach numbers 1 and 2 are equally important. Requirements: a) Derive the multi-point optimization formulation, i.e., ƒ as a function of x₁ and x₂ (30%) b) Solve the multi-point optimization problem and report the optimal objective function f* and design variable x*. (70%)