# Determine the max

Given:

Z=3x + 4y

From the given figure it is subject to constraints

x + 2y ≤ 76, 2x +y ≤ 104, x ≥ 0, y ≥ 0

Now let us convert the given inequalities into equation.

We obtain the following equation

x + 2y ≤ 76

x+2y=76

2x +y ≤ 104

2x +y = 104

x ≥ 0

x=0

y ≥ 0

y=0

The region represented by x + 2y ≤ 76:

The line x + 2y=76 meets the coordinate axes (76,0) and (0,38) respectively. We will join these points to obtain the line x + 2y=76. It is clear that (0,0) satisfies the inequation x + 2y ≤ 76. So the region containing the origin represents the solution set of the inequation x+2y≤76

The region represented by 2x +y ≤ 104:

The line 2x +y=104 meets the coordinate axes (52,0) and (0,104) respectively. We will join these points to obtain the line 2x +y=104. It is clear that (0,0) satisfies the inequation 2x +y ≤ 104. So the region containing the origin represents the solution set of the inequation 2x +y ≤ 104

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

The graph of these equations is given.

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

Corner Points are O (0, 0), D (0, 38), B (44,16) and A (52,0)

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

Hence, the maximum value of Z is 196 at the point (44,16).

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
RELATED QUESTIONS :

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