A logistics company needs to design a rectangular storage container with a square base. The container must have a volume of 36 cubic meters to efficiently store a specific product. The material cost for the base is \$80 per square meter, the material cost for the top is \$40 per square meter, and the material cost for the sides is \$60 per square meter.
a. Let $x$ be the side length of the square base and $h$ be the height of the container. Show that the total cost $C$ (in dollars) of the materials for the container can be expressed as $C = 120x^2 + \frac{8640}{x}$.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 3 marks, testing your understanding of Optimisation Problems. It falls under Calculus in Unit 4: Mathematical Methods Unit 4. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Continues the study of functions, algebra, calculus, and introduces probability and statistics.
Covers graphical treatment of limits, continuity and differentiability of functions of a single real variable, and differentiation, anti-differentiation and integration of these functions. This material is to be linked to applications in practical situations.
identification of local maximum/minimum values over an interval and application to solving optimisation problems in context, including identification of interval endpoint maximum and minimum values
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