Question

use branch and bound method to solve the following Lpp
maximize z=7x1+9x
27
32​

Answer 1

Answer:

The values, we can see that 7x+10y is maximum when x=30,y=20. The maximum value is 410

Step-by-step explanation:

From the above question,

The LPP given is:

Maximize 7x+10y subject to contsraints

4x + 6y ≤ 240

    =  x+3y≤120

6x + 3y ≤ 240

    =  2x + y ≤ 80

x ≥ 10

y ≥ 0

Plot the graphs of 2x + 3y = 120,

                                2x + y = 80,

                                        x = 10.

The shaded portion is the feasible region of the solution.

The corner points of the feasible region are (10,0),(40,0),(30,20) and

(10,$\frac{100}{3}$)

The feasible region is OAPQDO which is shaded in the figure.

The vertices of the feasible region are O (0,0), A 93,0), P, Q and D (0,3).

Pis the point of intersection of the lines x + y = 5, we get,

3+y=5

y=2

PP=(3,2)

Q is the point of intersection of the lines x + y = 5 , and y = 3

Substituting y = 3 in x+y=5, we get

x+3=5

x=2

Q = (2,3)

The values of the object function z = 10x + 25 y at these vertices are

Examining the objective function at these values:

From the values, we can see that 7x+10y is maximum when x=30,y=20. The maximum value is 410

For more related question : https://brainly.in/question/28467835

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