Math 157 Preparation for Optimization

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Terry makes and sells necklaces. He has observed over time that when the price is $9 each, he sells an average of 36 per day. If he increases the price, then his average sales fall by 3 per day for each dollar increase. The materials for each necklace cost $4. Express his prot P as a function of x, the number of necklaces sold. Answer: P(x) = If! A piece of wire: m long is cut into two pieces, the length of the rst piece being 18 m. The rst piece is bent into a circle, and the other is bent into a rectangle with length twice the width. Give an expression for the total area A enclosed in the two shapes in terms of x. Answer: A(x) = H You may wish to use the formula editor. A man can row at 15 kmfh, and run at 12 kmfh. He needs to get from a point A, on the south bank of a stretch of still water, to point B on the north bank of the water. The direct distance from A to B is 20 km, and the water is 16 km wide. He starts rowing with an angle 6' between North and the direction in which he rows. Find an expression for the time I he will take to get from A to B, in terms of 9. Answer: H9) = Note: To enter 6', write theta. If