Web Reference: Suppose you want to find out how big to make the cut-out squares in order to maximize the volume of the box. This applet will illustrate the box and how to think about this problem using calculus. The objectivefunction is the formula for the volume of a rectangular box: V=length×width×height=X×X×YV=X2Y The constraintequation is the total surface area of the tank (since the surface area determines the amount of glass we'll use). The surface area is simply the sum of the areas of the sides and bottom (the top is open). SA=X×X+XY+XY+XY+XYSA=X2+... One common application of calculus is calculating the minimum or maximum value of a function. For example, companies often want to minimize production costs or maximize revenue. In manufacturing, it is often desirable to minimize the amount of material used to package a product with a certain volume.
YouTube Excerpt: We solve a common type of
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