Hypothesis
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Yes. There need not be a feasible region.
It is definatly possible to have a no solution answer in algebra. The most common time a no solution answer will occur is in an absolute value problem. Absolute value problems cannot equal zero so if you have the problem: the absolute value of 2m - 3 = -14 the answer would be so solution because it cannot equal a negative number
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A problem and a solution are not synonyms or antonyms, but rather concepts that are related. A problem is a challenge or difficulty that needs to be solved, while a solution is the resolution or answer to that problem. They are not homophones, as they do not sound alike.
'optimal' means: best possible compromise solution to a problem, when there are several competing considerations, not all of which can be simulataneously maximized.