te ·Dr. Ann Watkins Applied Maximum/Minimum (1) A veterinarian has 100 feet of f

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te ·Dr. Ann Watkins Applied Maximum/Minimum (1) A veterinarian has 100 feet of fencing and wishes to construct six dog kennels by first building a fence around a rectangular region, and then subdividing that region into six smaller rectangles by placing five fences parallel to one of the sides. What (2)) A man in a boat 2 miles from the nearest point on the coast. He is to go to point Q. at 4 miles per hour, toward what point on the coast should he row in order to reach An underground TV cable is to be laid between two boat houses on opposite banks dimensions of the region will maximize the total area? 3 miles down the coast and I mile inland. If he can row at 2 miles per hour and walk point Q in the least time? note (3) of a straight river. One boathouse is 600 m downstream from the other. The river is 200 m wide. If the cost of laying cable is $50 per meter under water and $30 per meter on land, how should the cable be laid to minimize cost? (4) A page in a book is to have an area of 90 square inches, with 1-inch margins at the bottom and sides arda ½-inch margin at the top. Find the dimensions of the page which will allow the largest printed area. A rectangular page is to contain 24 square inches of print. The margins at the top and What should the dimensions of the page be so that the least amount of paper is used? (5) bottom of the page are each 1 ½ inches wide. The margins on eachhide are 1 inch. (6) An open box is to be made from a rectangular piece of material, by cutting equal squares from each comer and turning up the sides. Find the dimensions of the box of maximum volume if the material has dimension of 2 feet by 3 feet.. A wire 36 cm long is to be cut into two pieces. One of the pieces will be beint into the shape of an equilateral triangle and the other into the shape of a rectangle whose length is twice its width. Where should the wire be cut if the combined area of the (7) triangle and rectangle is a (a) minimum? (b) maximum? A window has the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the window is 12 feet, find the dimensions of the rectangle that will (8) produce the largest area for the window. (Approximate.) An indoor physical fitness room consists of a rectangular region with a semicircle on each end. If the perimeter of the room is to be a 200-meter running track, find the dimensions that will make the area of the rectangular region as large as possible. (9) Find the dimensions of the rectangular box of the greatest volume that can be constructed from 100 square inches of cardboard (surface area) if the base is to be (10) twice as long as it is wide.

Explanation / Answer

You will have to post all the questions separately. As per chegg policy, I will answer only one question per post.

let's say the dimnesion of the rectangular regions are b and l.

fence will be constructed on perimeter of rectangle and perimeter is 2 (b+l) and

2 (b+l) = 100

b+l = 50

b = 50 - l

now the this rectangular region will be divided into 6 smaller part (kennels or smaller rectangle)

let's the division is done across length so area of each of this kennel (b,l/6) = b*l/6

total area = 6*bl/6 = b*l

total area = l (50-l) = 50l-l2

first derivative is 0 for maxima.

50 - 2l = 0

l = 25

b = 25

so it is a square.

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