Question
An open-topped box is to have a square base and a volume of 10 ?3. The...
An open-topped box is to have a square base and a volume of 10 ?3. The cost per square meter of material is $5 for the bottom and $2 for the four sides. Let ? be the length of the base of the box and ℎ be the height of the box. Let ? be the total cost of material required to make the box.
a. Express ? as a function of ? and find its domain.
b. Find the dimensions of the box so that the cost of materials is minimized. What is the minimum cost? Be sure to show why your answer gives a global minimum.
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