MathDB
Maximizing Diophantus

Source:

March 21, 2008
inequalities

Problem Statement

Let A A, M M, and C C be nonnegative integers such that A \plus{} M \plus{} C \equal{} 12. What is the maximum value of A \cdot M \cdot C \plus{} A\cdot M \plus{} M \cdot C \plus{} C\cdot A? <spanclass=′latex−bold′>(A)</span> 62<spanclass=′latex−bold′>(B)</span> 72<spanclass=′latex−bold′>(C)</span> 92<spanclass=′latex−bold′>(D)</span> 102<spanclass=′latex−bold′>(E)</span> 112 <span class='latex-bold'>(A)</span>\ 62 \qquad <span class='latex-bold'>(B)</span>\ 72 \qquad <span class='latex-bold'>(C)</span>\ 92 \qquad <span class='latex-bold'>(D)</span>\ 102 \qquad <span class='latex-bold'>(E)</span>\ 112
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