Let's do some calculus! (46)

Calculus Level 5

If the maximum value of

\[\large f(x,y,z) = 2x^2 + 3y - 4z \]

subject to the constraints

\[\begin{cases} 2x-4y-2z=5 \\ x^2+y^2 = 1 \end{cases}\]

is equal to \(M\), then evaluate \(\left\lfloor M \right\rfloor\).

Note: It is advised to take the aid of a calculator for mathematical computations in this problem.

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