Solve the following optimization problems 9. Make an open box from a square cardboard with sides measuring36 cm by cutting equal squares out of the corners turning thesides. Find the dimensions of the box that will give the maximumvolume.10. From a piece of cardboard that is 24 cm by 48 cm, cut equalsquares out of the corners. Fold up the sides to form an openbox. Determine the height of the box that will give the maximumvolume.11. A rectangular chicken pen is bounded on one side by the wall ofthe house and the other three sides by 160 meters of fences. Findthe dimensions of the chicken pen if the area is a maximum.

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Answered: 9. Make an open box from a square…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Yet another (fictional) student submitted the following solution to an optimization problem. This time the solution is technically correct, but it is still insufficient there isn't nearly enough detail/explanation to receive full credit. Rewrite the solution below, adding all details (including a diagram) that are necessary to produce a complete solution worthy of full marks. (To be clear: the final answer is correct. What we want to see are the necessary explanations to make it clear where each step is coming from.) Problem: Find the dimensions of the rectangle of maximum area that can be drawn within a semicircle of radius 3, if one side of the rectangle lies along the diameter of the semicircle. (Suggestion: draw your semicircle on the ry-plane as the top half of the circle ? + y? = 9.) Solution: A = 2ry = 2r9-a A' = 2/9-2 272 2(9 - 22?) V9-2 2x = 9 so r Dimensions: 2x = 3/2 and y =
I need help finding the answers to this optimization problem and an explanation on how to find them.
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In this question, you will work step-by-step through an optimization problem. Many airlines restrict the size of carry on item in terms of their combined length, width and height (L+W+H). I am due to fly on an airline that states "The sum of the length, the width and height of your item must be at most 50 inches". Suppose I want to take a box (cuboid) on my trip that will allow me to carry on as much as possible, and that I also want this box to have a square base. The questions we will answer using optimization are: What dimensions should the box have, and what would be the resulting maximum volume? If the base of the box is a square whose sides have length x, and the height of the box is h (both measured in inches), enter expressions for the volume of the box, V, and the sum of the length, width and height of the box in terms of x and h. V : Sum L+W+H : Since the sum of the length, width and height must be less than or equal to 50 inches, and it is clearly best to choose this…
Find the dimensions of the rectangular box with largest volume such that the sum of the lengths of its twelve edges is 24. You may do this using either of the optimization techniques we learned in class, but you must justify your answer.
I need both parts handwritten it's one question only i swear if you do only one part dislike is for sure otherwise if done both I'll like

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9. Make an open box from a square cardboard with sides measuring 36 cm by cutting equal squares out of the corners turning the sides. Find the dimensions of the box that will give the maximum volume.