Minimum value

Algebra Level 3

Consider all integer values of a a and b b for which a < 2 a < 2 and b ≥ − 2 b \ge -2 . What is the minimum value of b − a b - a ?


The answer is -3.

Marvin Kalngan by Marvin Kalngan , 38, Philippines

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1 solution

Tom Engelsman
Apr 18, 2021

If we plot out the feasible region of this Integer Linear Program, we have an infinite rectangle with the single critical point ( a , b ) = ( 2 , − 2 ) (a,b) = (2,-2) . Since a ∈ ( − ∞ , 2 ) a \in (-\infty, 2) , the largest positive integer is a = 1 a = 1 . This gives us the minimum value b − a = − 2 − 1 = − 3 . b-a = -2 -1 = \boxed{-3}.

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