Question

sᴏʟᴠᴇ ᴛʜᴇ ғᴏʟʟᴏᴡɪɴɢ ʟɪɴᴇᴀʀ ᴘʀᴏɢʀᴀᴍᴍɪɴɢ ᴘʀᴏʙʟᴇᴍ ɢʀᴀᴘʜɪᴄᴀʟʟʏ:

ᴍɪɴɪᴍɪsᴇ ᴢ = 200 x + 500 ʏ sᴜʙᴊᴇᴄᴛ ᴛᴏ ᴛʜᴇ ᴄᴏɴsᴛʀᴀɪɴᴛs:

x + 2ʏ ≥ 10

3x + 4ʏ ≤ 24

x ≥ 0, ʏ ≥ 0

​

Answer 1

Answer:

x+2y>=10. .....eqn 1

3x+4y<=24......eqn2

x>=0,y>=0.... eqn 3

z=200x+500y......eqn4

Step-by-step explanation:

let eqn 1,x+2y=10 divide throughout by 10

x/10+y/5=1... intercepted form

here a=10,b=5

let p(x,y)where x and y is zero

therefore,eqn 1become

0>=10 which is true hence solution lie towards the origin

.let eqn 2,3x+4y=24divide throughout by 24

we get,

x/8+y/6=1.....which is intercepted form

here c=8 and d=6

let p be test point where x and y is equal to zero

therefore eqn 2become,

0<=24 which is true hence solution lie towards the origin

from eqn3 solutin lie in first quadrent

Now, draw a graph on the value of a,b,c,,d and note the freezing point or intersection point{E(x,y)} where all the line intersect

equate eqn 1and2 you get the value of x and y of E

then put all the value in eqn....4

you get the required answer

HOPE IT WILL HELP YOU IN YOUR STUDY'S ✌️

Answer 2

Answer:

sᴏʟᴠᴇ ᴛʜᴇ ғᴏʟʟᴏᴡɪɴɢ ʟɪɴᴇᴀʀ ᴘʀᴏɢʀᴀᴍᴍɪɴɢ ᴘʀᴏʙʟᴇᴍ ɢʀᴀᴘʜɪᴄᴀʟʟʏ:

ᴍɪɴɪᴍɪsᴇ ᴢ = 200 x + 500 ʏ sᴜʙᴊᴇᴄᴛ ᴛᴏ ᴛʜᴇ ᴄᴏɴsᴛʀᴀɪɴᴛs:

x + 2ʏ ≥ 10

3x + 4ʏ ≤ 24

x ≥ 0, ʏ ≥ 0