Question

7). Given the following LP problem
Maximize Z= 4X + 6Y
Subject to:
2X + 3Y ≤ 150
4X + 2Y ≤ 80
with X, Y≥ 0​

Answer 1

Step-by-step explanation:

12th

Maths

Linear Programming

Graphical Solution of a Linear Programming Problems

Consider the following L.P....

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Asked on October 15, 2019 by

Loveleen Hasan

Consider the following L.P.P.

Maximize Z=3x+2y

Subject to the constraints

x+2y≤10

3x+y≤15

x,y≥0

(a) Draw its feasible region.

(b) Find the corner points of the feasible region.

(c) Find the maximum value of Z.

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ANSWER

(a)

Z=3x+2y .......... (i)

subject to the constraints

x+2y≤10

3x+y≤15

Convert these inequalities into equations

x+2y=10 ......... (ii)

3x+y=15 ......... (iii)

From (ii), we get

x=0⟹y=5 and y=0 when x=10

So, the points (0,5) and (10,0) lie on the line given in (ii)

From (iii), we get the points

(0,15) and (5,0)

Let's plot these point and we get the graph in which, shaded part shows the feasible region.

(b)

Lines (ii) and (iii) intersect at (4,3) and other corner points of the region are (0,5),(5,0) and (0,0).

(c)

To find the maximum value of z, we need to find the value of z at the corner points

Corner points z=3x+2y

(0,0) 0

(5,0) 15

(0,5) 10

(4,3) 18

Thus, z is maximum at (4,3) and its maximum value is 18.