Determine a minimal solution of the optimization problems: (a) min (x − 3)2 + (y − 2)2 subject to the constraints x2 + y2 ≤ 5 x + y ≤ 3 x ≥ 0, y ≥ 0. (b) min (x − 9 4 )2 + (y − 2)2 subject to the...

Determine a minimal solution of the optimization problems:

(a) min (x − 3)2 + (y − 2)2

subject to the constraints

x2 + y2 ≤ 5

x + y ≤ 3

x ≥ 0, y ≥ 0.

(b) min (x − 9

4 )2 + (y − 2)2

subject to the constraints

x2 − y ≤ 0

x + y − 6 ≤ 0

x ≥ 0, y ≥ 0.

(c) max 3x − y − 4z2

subject to the constraints

x + y + z ≤ 0

−x + 2y + z2 = 0

x,y,z ∈ R.