Question

Chp No :
Name : LINEAR PROGRAMMING PROBLEM
192) The maximum value of Z = 3x + 4y subjected to constraints x + y <= 40, x + 2y<= 60, x>=0 nd y >= 0 is
A) 120
C) 100
B) 140
D) 160​

Answer 1

Answer:

140

Step-by-step explanation:

Z=3x+4y

constraints:

x+y≤40

x+2y≤60

x≥O y≥0

equations for x and y

x+y=40

@x=0 y=40

@y=0 x=40

x+2y=60

@x=0 y=30

@y=0 x=60

feasible region:ABCD

A (0,30)

B (20,20)

C (0,0)

D (40,0)

Z@ (0,30)

3(0)+4(30)=120

Z@ (20,20)

3(20)+4(20)=140

Z@(0,0)

0

Z@(40,0)

3(40)+4(0)=120

therefore maximum value of Z is @ B (20,20)

140

*you can draw the graph using desmos graphing app available on playstore*