Study the family of inequalities aligned x + k y &0 k = 2 x + k y < 4 x + k y 4$…
MATHEMATICS · Subjective · CBSE · Mathematics · Linear Inequalities · Linear Inequalities
Problem
Study the family of inequalities
x+ky2x+yxy<4,≤6,≥0,≥0,
where k is a positive real parameter.
(i) For the inequality x+ky<4, state the style of its boundary line for any k>0 and justify your answer.
(ii) Taking k=2, sketch the complete feasible region determined by the four inequalities and identify every boundary as solid or dashed.
(iii) Discuss qualitatively how the feasible region would change if the inequality x+ky<4 were replaced by x+ky≤4 while keeping all other constraints unchanged.