A production planner works with the following system of constraints on the decision…
MATHEMATICS · Multi-part · CBSE · Mathematics · Linear Programming · Linear Programming
Problem
A production planner works with the following system of constraints on the decision variables x and y:
x+2y≤10,
x≥0, y≥0.
She decides to change only the first inequality to
x+4y≤10,
leaving the non-negativity restrictions unchanged.
Qualitatively analyse how this single change affects the feasible region without actually plotting precise graphs.
(i) Calculate the x- and y-intercepts of the boundary lines corresponding to the inequality before and after the change.
(ii) Explain how the slope of the boundary line changes and what that implies about the orientation of the feasible half-plane.
(iii) State whether the new feasible region is a subset of, a superset of, or incomparable with the original feasible region. Justify your answer.
(iv) Comment, with reason, on how the area of the feasible region is affected by the change.