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# Calculus of Functions of One Variable I MATH 231

UNC

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This 2 page Class Notes was uploaded by Dovie Hyatt on Sunday October 25, 2015. The Class Notes belongs to MATH 231 at University of North Carolina - Chapel Hill taught by Brenda Shryock in Fall. Since its upload, it has received 43 views. For similar materials see /class/228747/math-231-university-of-north-carolina-chapel-hill in Mathematics (M) at University of North Carolina - Chapel Hill.

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Date Created: 10/25/15

Math 231 O 00 D Shryock MAX MIN Word Problems A rectangular field is to be enclosed by a fence and divide into 3 lots by fences parallel to one of its sides Find the dimensions of the largest field that can be enclosed with a total of 800 meters of fencing A farmer wishes to enclose a 4000 square meter field and subdivide the field into four rectangular plots with fences parallel to one of the sides What should be the dimensions of the field be in order to minimize the amount of fencing required An open box is formed from a square sheet of cardboard by cutting equal squares from each corner and folding up the edges If the dimensions of the cardboard are 18 cm by 18 cm what should be the dimensions of the box so as to maximize the volume and what is the maximum volume An open box is formed from a rectangular sheet of cardboard by cutting equal squares from each corner and folding up the edges If the dimensions of the cardboard are 15 in by 24 in what size squares should be cut to obtain a box of maximum volume A box is made with a square bottom and open top to hold a volume of 8 cubic feet The material for the sides costs 4 per square foot and the material for the bottom costs 1 per square foot What dimensions will minimize the cost of the box A car rental agency has 24 identical cars The owner of the agency finds that at a price of 10 per day all the cars can be rented However for each 1 increase in rental price one of the cars is not rented How much should be charged to maximize the income to the agency Suppose a rectangle has its lower base on the x axis and upper vertices on the graph of the function y 8 x2 Find the area of the largest such rectangle A right triangle of hypotenuse 10 units is rotated about one of it legs to generate a right circular cone What is the greatest possible volume of this cone Find the base radius r and the height h of the right circular cone of maximum volume that will fit inside a sphere of radius 3 units A motorist is in the desert in a Jeep The closest point on a straight road is town A and it is 4 miles from the motorist He wishes to reach town B 10 miles from town A on the road in the shortest time If he can drive 15 mihr on the desert and 45 mihr on the road where should he intersect the road

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