(Solved): only b option ?? 2. The economy of Northern Saskatchewan is in equilibrium w ...

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only b option ??

2. The economy of Northern Saskatchewan is in equilibrium when the system of equations \( 2 x z+x y+z-2 \sqrt{z}=11 \) and \( x y z=6 \) is satisfied. One solution of this set of equations is \( \left(x^{*}, y^{*}, z^{*}\right)=(3,2,1) \) and the economy is equilibrium at this point. Suppose that the prime minister discovers that the variable \( z \) can be controlled by a simple decree. a) If the prime minister raises \( z \) to \( 1.1 \), use differential calculus to estimate the change in \( x \) and \( y \) simultaneously. (10 points) b) If \( x \) were in the control of the prime minister and not \( y \) or \( z \), explain why you cannot use this method to estimate the effect of reducing \( x \) from 3 to \( 2.95 \). (15 points)