# Find graphically,

Given,

Objective function is: z = 2x + 5y

Constraints are:

2x + 4y ≤ 8

3x + y ≤ 6

x + y ≤ 4

x ≥ 0, y ≥ 0

the maximum value of z can only be obtained at the corner points of the feasible region. So we need to check the value of z at all corner points of the feasible region.

So, first, we will be finding out the feasible region by drawing the regions defined by constraints.

For plotting feasible region, we will be using the fundamentals of a straight line to get the feasible region as shown in the figure. Clearly ABDC represents the feasible region and corner points are determined by solving:

3x+y = 6 and 2x + 4y = 8

x = 0 and 2x+4y = 8

y = 0 and 3x+y = 6

& x = 0 and y = 0

value of objective function z at point A = Value of Z at point B = 2× 2 + 0 = 4

Value of Z at point C = 2× 0 + 5× 2 = 10

Value of Z at point B = 2×0 + 0 = 0

Clearly Z is maximum at point C(0,2)

And maximum value of Z = 10

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 :

A manufacturer prMathematics - Board Papers

A retired person Mathematics - Board Papers

A manufacturing cMathematics - Board Papers