Answer :


Z=3x + 4y

It is subject to constraints

x + y ≤ 1, x ≥ 0, y ≥ 0

Now let us convert the given inequalities into equation.

We obtain the following equation

x + y ≤ 1

x + y=1

x ≥ 0


y ≥ 0


The region represented by x+y≤1:

The line x + y=1 meets the coordinate axes (0,1) and (1,0) respectively. We will join these points to obtain the line x + y=1. It is clear that (0,0) satisfies the inequation x+y≤1. So the region containing the origin represents the solution set of the inequation x+y≤1

Region represented by x≥0 and y≥0 is first quadrant, since every point in the first quadrant satisfies these inequations.

Plotting these equations graphically, we get

The shaded region OBC shows the feasible region is bounded, so, maximum value will occur at a corner point of the feasible region.

Corner Points are O (0, 0), B (0, 1) and C (1, 0).

Now we will substitute these values in Z at each of these corner points, we get

Hence, the maximum value of Z is 4 at the point (0, 1).

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses

Corner points of Mathematics - Exemplar

Using the method Mathematics - Board Papers

Refer to ExerciseMathematics - Exemplar

A dietician wisheRD Sharma - Volume 2

A merchant plans Mathematics - Board Papers

A dietician wisheMathematics - Board Papers

Maximise and MiniMathematics - Exemplar