Solve the LP problem If no optimal solution exists indicate

Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. Maximize p = 3x + y subject to 5x - 7y = 0 x+ y 0, y > 0. P = (x, y) =

Solution

Given that

P=3x+y

Let take that 5x-7y=0,7x-5y=0and x+y=12from the problem for esay to slove

5x-7y=0....(1)

7x-5y=0....(2)

x+y=12...(3)

Add equations (1)+(3) and (2)+(3)

Adding (1)+(3)

(5x-7y=0)+(x+y=12)={6x-6y=12}=6(x-y)=12

x-y=2....(4)

Addind (2)+(3)

(7x-5y=0)+(x+y=12)={8x-4y=12}={4(2x-y)=12}

2x-y=3...(5)

Now subtract equations (5)-(4)

{[2x-y=3]-[x-y=2]}={x-0=1}

x=1...

Substitute x=1in any equation to find y

Let us take equation 5

2x-y=3

2*(1)-y=3

-y=3-2

y=-1

Therefore (x,y)=(1,-1)

P=3x+y

P=3*1+(-1)

=3-1

=2