Consider the following linear programming problem

Maximize Px_{1}+x_{2} 

Subject to x_{1}+2x_{2}\geq 14,3x_{1}+x_{2}\geq 3,x_{1}+6x_{2}\geq16,x_{1},x_{2}\geq 0

For which values of P is there no solution to this problem?

  • Option 1)

    P=0

  • Option 2)

    P<0

  • Option 3)

    P=2

  • Option 4)

    P>0

 

Answers (1)

As we learnt in 

Decision Variables -

In Z = ax+by, x and y are decision variables. 

-

 

for Z=Px_{1}+x_{2}

  = 0+7 at (0,7)

Z = 16 P + 0 = 16 P at (16, 0)

z= 12P + \frac{1}{2}at (12, \frac {1}{2})

so that for 16P,\ P \geq0. 

So far P <O  it has no solution.

 

 


Option 1)

P=0

Incorrect

Option 2)

P<0

correct

Option 3)

P=2

Incorrect

Option 4)

P>0

Incorrect

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