Optimization Problems

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Presentation transcript:

Optimization Problems Section 3.7 Optimization Problems

A manufacturer wants to design an open-top box having a square base and a surface area of 108 square inches. What dimensions will produce a box with maximum volume? → Primary Equation → Secondary Equation h x x _ + 6 Dimensions are 6 x 6 x 3

Which points on the graph of are closest to (0, 2)? (x, y) _ _ + +

A rectangular page is to contain 24 square inches of print A rectangular page is to contain 24 square inches of print. The margins on the top and bottom are to be 1.5 inches and the margins on the left and right are to be 1 inch. What should the dimensions of the total page be so that the least amount of paper is used? 1.5 in 1 in 1 in A = 24 y y + 3 x 1.5 in X + 2

_ + 4

Four feet of wire can be used to form a square and a circle Four feet of wire can be used to form a square and a circle. How much wire should be used for each if you want to enclose a maximum total area?

_ + 0.56 But we want a maximum?

If all wire is used for square If all wire is used for circle So all of the wire should be used for the circle.