#### Linear programming

Q. No. 3

Let number of black TV=X

Number of white TV  =Y

Now Number to TV are =250

X+Y= 250-----------------I

Total amount to be spend =414000

Cost of making one black TV =1500

Cost of making one white TV =1800

Therefore 1500X+1800Y=414000----------------------------II

Now , Profit=Profit on X+ Profit on Y

Profit =500X+600Y------------------iii

After solving i and ii we will get

X= 120,  Y=130    ( 1st  POINTS)

Take first equation put X=0 then Y=250      , if we put Y=0 then X=250

So we have X=0, Y=250   (2nd Points

And Y=0 , X =250 (3rd  Points )

Similarly from 2nd Equation  If we put X =0, Y=230  and If we put Y=0 then X =276

So we Have X=0,Y=230( 4th Points)

Y=0, X=276 ( 5th points)

Point the values of pint in equation  iii

X= 120,  Y=130       Profit=1500*120+1800*130=180000+234000=414000

X=0, Y=250           Profit=1500*0+1800*250=0+450000=450000 (maximum)

Y=0 , X =250        Profit=1500*250+1800*0=375000+0=375000

X=0,Y=230           Profit=1500*0+1800*230=0+414000=414000

Y=0, X=276          Profit=1500*276+1800*0=414000+0=414000

*Plot all point on graph paper