Following is an infeassible solution for the linear programming model given below:

Maximize, Z=x_{1}+2x_{2}

Subject to constraint 1:x_{1}+x_{2}\leq 5

Constraint 2 2:x_{1}+3x_{2}\leq 9

  • Option 1)

    \left ( x_{1},x_{2} \right )= \left ( 1,3 \right )

  • Option 2)

    \left ( x_{1},x_{2} \right )= \left ( 1,1 \right )

  • Option 3)

    \left ( x_{1},x_{2} \right )= \left ( 3,1 \right )

  • Option 4)

    None\, \, of \, \, the\, \, above

 

Answers (1)

As we learnt in 

Corner Point Method -

This method of solving a LPP graphically is based on the principle of extreme points theorem.

-

 

 

 Z=x_{1}+2x_{2}

 x_{1}+x_{2}\leq 5

 x_{1}+3x_{2}\leq 9

x_{1}=3

x_{2}=2

\\ z= 1+6 =7 \ at (1, 3)\\ = 1+2 = 3 \ at (1, 1) \\ = 3 + 2 =5 \ at (3, 1)

At (1,3), it is maximum 


Option 1)

\left ( x_{1},x_{2} \right )= \left ( 1,3 \right )

Correct

Option 2)

\left ( x_{1},x_{2} \right )= \left ( 1,1 \right )

Incorrect

Option 3)

\left ( x_{1},x_{2} \right )= \left ( 3,1 \right )

Incorrect

Option 4)

None\, \, of \, \, the\, \, above

Incorrect

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