Mathematics

Problem

For the linear programming problem Maximise

Z = kx - y

subject to

x \ge 0,\; y \ge 0,\; x + y \ge 4,\; x + 3y \ge 6

, for which values of the parameter

k

does the problem have a finite maximum value? a)

k \ge 0

k < 0

k \le 0

-1 \le k \le -\dfrac{1}{3}