Mathegoras

Calculus › Optimisation problems › Boxes of maximum volume

Largest edge of a box

High school · ●●●○○ 50 pts

An m×n×pm\times n\times p rectangular box has half the volume of an (m+2)×(n+2)×(p+2)(m + 2)\times(n + 2)\times(p + 2) rectangular box, where m,n,m, n, and pp are positive integers with m≤n≤pm\le n\le p. Find the largest possible value of pp.

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Diophantine equationsfactoringinteger optimizationinequalities