Which of the following LP problems has an optimal solution?

Note: In all cases x_{1}\geq 0,x_{2}\geq 0

  • Option 1)

    Min -2x_{1}+x_{2} subject to x_{2}\leq2

  • Option 2)

    min -2x_{1}+x_{2} subject to x_{1}+x_{2}\geq 5,2x_{1}+x_{2}\geq 7

  • Option 3)

    Max \, \, 2x_{1}+x_{2} subject to x_{1}-x_{2}\leq 2

  • Option 4)

    None of these

 

Answers (1)

As we learnt in 

Solution of a LPP -

A set of values of the variables x_1, x_2, x_3..................x_n satisfying the constraints of a LPP.

-

 

for max or min optimal solution

two linear equations must be taken

for xand x2

 


Option 1)

Min -2x_{1}+x_{2} subject to x_{2}\leq2

Incorrect

Option 2)

min -2x_{1}+x_{2} subject to x_{1}+x_{2}\geq 5,2x_{1}+x_{2}\geq 7

correct

Option 3)

Max \, \, 2x_{1}+x_{2} subject to x_{1}-x_{2}\leq 2

Incorrect

Option 4)

None of these

Incorrect

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