A rancher plans to fence-in a rectangular corral adjacent to a river for a herd of cattle. The rancher has supplies for 1,000 meters of fence. Use algebra and the methods of this class to determine the dimensions and area of the corral of maximum area, assuming all fencing supplies are used. Do not use
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- A box with a square base and an open top is being constructed out of A cm^2 of material. If the volume of the box is to be maximized, what should the side length of the base be? What should the height of the box be? What is the maximal volume of the box? Your answers should be in terms of A.The back of Jill's property is a creek. Jill would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a corral. If there is 880 feet of fencing available, what is the maximum possible area of the corral?Farmer S. Unkist has a fruit grove consisting of lemons, bananas, and watermelons along a straight moat. To prevent thieves from stealing his fruit while at the same time make sure the fruit do not mix before they are processed, he plans to fence in each fruit plot using identical rectangular enclosures. The side along the moat needs no fence because the moat is infested with man eating crocodiles as shown below. If he has 1200 yards of fence, what should be the dimensions of each enclosure if the total area of the grove is to be maximized? PLEASE USE CALCULUS TECHNIQUES TO OBTAIN YOUR ANSWER AND SHOW ALL WORK.
- If an isosceles triangle has perimeter P, how long must the legs of the triangle be to maximize its area? (Your answer may depend on P).A Norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular Norman window is to be 20 feet. What should the rectangle's dimensions be in order to maximize the area of the window and, therefore, allow in as much light as possible? The answer to this question is in two parts: first, the width of the rectangle in feet and second, the height of the rectangle in feet.A three-sided fence is to be built next to a straight section of river, which forms the fourth side of a rectangular region. The enclosed area is to equal 242 m2. Find the minimum perimeter and the dimensions of the corresponding enclosure. Dimensions: = ____ m x ____ m Minimum perimeter: = ____ m
- The back of Dante's property is a creek. Dante would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a corral. If there is 760feet of fencing available, what is the maximum possible area of the corral?A) given the perimeter of the rectangle is 100 meters. What is the dimension should be to get the maximum area? B) Given the area of a rectangle is 64 square meters. What dimension should be to get the minimum perimeter?Need help in business calculus. If a rectangle with length and width (in ft) has a perimeter of 361 ft, what is the length and width of the rectangle with a minimum perimeter and how do I find the minimum perimeter of the rectangle?
- A lifeguard needs to rope off a rectangular swimming area in front of Long Lake Beach, using 500yd of rope and floats. What dimensions of the rectangle will maximize the area? What is the maximum area? (Note that the shoreline is one side of the rectangle.)A wire is to be cut into two pieces. One piece will be bent into an equilateral triangle, and the other piece will be bent into a circle. If the total area enclosed by the two pieces is to be 81 m^2, what is the minimum length of wire that can be used? Find Lmin and Lmax.In an orchestra, 23 people can play stringed instruments, 21 can play brass, and 15 can play percussion. Further, 9 of the performers can play both strings and brass, whereas 8 can play both strings and percussion. If no one can play all three types of instruments, what are the maximum and minimum numbers of people in the orchestra? (Hint. Consider expressing the numbers in some of the regions of your diagram in terms of a single unknown, say x.)