Math Problem Statement

A rectangular storage container with an open top is to have a volume of 18 cubic meters. The length of its base is twice the width. Material for the base costs $11 per square meter. Material for the sides costs $8 per square meter. Find the cost of materials for the cheapest such container.

Solution

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Math Problem Analysis

Mathematical Concepts

Optimization
Geometry
Calculus

Formulas

Volume = length × width × height
Area of base = length × width
Surface area of sides = 2 × (length × height) + 2 × (width × height)
Cost = (base area × base material cost) + (side area × side material cost)

Theorems

Optimization using calculus
Derivatives for finding minima

Suitable Grade Level

Grades 11-12 or early college

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