Is a unit disk D1 x x12 x22 lessthanorequalto 1 a polyhedr

Is a unit disk D_1 = {x: x_1^2 + x_2^2 lessthanorequalto 1} a polyhedron? b. Define a feasible set(feasible region) of a linear optimization problem. c. Can a unit disk D_1 above be a feasible region of a linear optimization problem?

Solution

(a) No. The unit disk D₁ is not a polyhedron. (generally a polyhedron is formed by faces that formed by edges and vertices)

(b) In an optimization (linear/nonlinear) problem, the feasible region or feasible set is set of all points (set of all values of decision variables) that satisfies all of the constraints (linear equations or inequalities) of the problem.

c) The unit disk D₁canot be a feasible region, because a feasible region is a polyhedron formed by all of the constraints of the linear optimization problem