For the constraints

MATHEMATICS · Subjective · CBSE · Mathematics · Linear Programming · Linear Programming

Problem

For the constraints

x + y \ge 3,\; 2x + y \ge 4,\; x \ge 0,\; y \ge 0

, consider the objective function

Z = kx + y

to be minimised, where

k

is a real parameter. Determine all values of

k

for which a finite minimum value of

Z

exists.