The inequalities determine a feasible region in the first quadrant

MATHEMATICS · Single correct · CBSE · Mathematics · Linear Programming · Linear Programming

Problem

The inequalities

x + y \le 8,\; x \ge 0,\; y \ge 0

determine a feasible region in the first quadrant. You wish to maximise the objective function

Z = kx + y

, where

k

is a real parameter. Which one of the following statements is correct regarding the finiteness of the maximum value of

Z

? (a) The maximum is finite only if

k>0

. (b) The maximum is finite for every real

k

. (c) The maximum is finite only if

\lvert k\rvert \le 1

. (d) The maximum is never finite for any real

k