Q. 24.4( 43 Votes )

# Minimise Z = – 3x + 4 y subject to x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0.

Answer :

It is given in the question that,

Z = - 3x + 4y

We have to subject on the following equation:

x +2y ≤ 8, 3x+2y ≤ 12, x ≥ 0, y ≤ 0

3x+2y ≤ 12

(x, y) = (0, 6), (4, 0)

x+2y ≤ 8

(x, y) = (0, 4), (8, 0)

We can clearly see that Z is minimum at (4, 0). Hence, minimum value of Z will be - 12

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

Related Videos

Range of Quadratic/quadratic & linear/Linear functions45 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation

RELATED QUESTIONS :

Using the method of integration, find the area of the region bounded by the following lines:

5x - 2y - 10 = 0

x + y - 9 = 0

2x - 5y - 4 = 0

Mathematics - Board PapersRefer to Exercise 27. (Maximum value of Z + Minimum value of Z) is equal to

Mathematics - ExemplarMaximise and Minimise Z = 3x – 4y

subject to x – 2y ≤ 0

– 3x + y ≤ 4

x – y ≤ 6

x, y ≥ 0

Mathematics - Exemplar