Mathematics

Problem

The constraints

x \ge 0,\; y \ge 0,

and

x + 2y \le 10

define a feasible region that lies below the line

x + 2y = 10

. If the first inequality is replaced by

x + 2y \ge 10

while the other two remain unchanged, which statement correctly describes the new feasible region? a) The feasible region shifts to the half-plane

x+2y \ge 10

while still confined to

y \ge 0

. (It therefore lies above the line.) b) All feasible points now lie exactly on the line

x+2y = 10

with

y \ge 0

(i.e. the ray of the line from

(10,0)

upward). c) The three inequalities are contradictory, so the feasible region is empty. d) Because the inequality sign became “

\ge

”, the boundary

x+2y=10

is no longer included; it should be drawn dashed.