Math Problem Statement
A box is constructed so that its length is twice its width. The sum of its length, width and depth is 140 cm. Calculate the values for its dimensions which result in a maximum surface area. Calculate this maximum surface area
Solution
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Math Problem Analysis
Mathematical Concepts
Algebra
Optimization
Derivatives
Surface Area Calculation
Formulas
Surface area of a box: A = 2lw + 2lh + 2wh
Derivative of a quadratic function: A'(w) = -28w + 840
Theorems
Optimization using derivatives
Quadratic maximization
Suitable Grade Level
Grades 10-12
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