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Can anyone please help me on this?

Maximize: ax+by

Subject to:

x-y>=2

-x+2y>=4

Find values of a and b for which the above LP has a feasible solution.

I plotted the region but I am not confident of my answer. I am confused between two answers (both could be wrong):

  • Would the cost function be parallel to one of the constraint conditions for the LP to have a feasible solution?

  • Or would any positive value of a and b would be sufficient for the LP to have a feasible region?

Thanks for your help!

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    Whether a feasible solution exists depends on the inequalities, not on $a$ and $b$. Just check whether the inequalities can simultaneously hold. – 2017-02-20
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    Whether an optimal solution exists (and whether it is unique) will probably depend on $a$ and $b$ – 2017-02-20
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    So how do I find the values of a and b for which I do get a feasible region? – 2017-02-20
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    They do not matter. This is what confuses me. The exercise indicates that they should matter. – 2017-02-20
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    I know, its quite confusing. I have been reading a lot but am not about to reach to an answer. – 2017-02-20

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