Find the Maximum and Minimum Volumes of a Rectangular Box

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A height of 5 inches produces the box with maximum volume 2000 cubic inches.

. -- x 650-λ2 2λ xyz50 ------- x50-2λ. C t cos t sin t. Answer Maximum volume is 3534 c m 3 Minimum volume is 2948 c m 3 View Answer More Answers 0927 WZ Wen Z.

C t cos t 8 sin t. What is the maximum volume you could have for a rectangular box if you are given its surface area. Find the maximum and minimum volumes of a rectangular box whose surface area is 1500 cm3 and whose total edge length is 200 cm.

42 Find the maximum and minimum volumes of a rectangular box whose surface area is 1500 cm2 and whose total edge length is 200 cm. Step 1 of 3 The objective is to find the maximum and minimum volumes of a rectangular box using Lagrange multipliers. Write down the function you want to maximize and the two constraint functions.

Find the maximum and minimum volumes of a rectangular box whose surface area is 1500 cm2 and whose total edge length is 200 cm. It can be deduced that the box is not a cube so if x y and z are the lengths of the sides you may want to let x represent a side with and. The trick is to gure out how to solve these equations.

Then using that info to solve we get. Get the answer to your homework problem. This video shows you how to do it using calculus if you ar.

Next write down the system of equations for the Lagrange multipliers method. 0 t 2 π maximum value_____ minimum value_____. V a b c λ p a ρ q a λ b c ρ V_a bc lambda p_arhotimes q_a lambdabcrho V a b c λ p a ρ q a λ b c ρ.

Find the maximum and minimum volumes of a rectangular box whose surface area equals 8000 square cm and whose edge length sum of lengths of all edges is 480 cm. Yzλ yzμ 1 xzλ xzμ 2 xyλ xyμ 3 1- 2 implies λz while 1- 3 implies λy. Maximum value is.

Find the maximum and minimum values attained by the function f along the path c t. Maximum value is а occuring at en. It can be deduced that the box is not a cube so if x y and z are the lengths of the sides you may want to let x represent a side with x y and x z.

A f x y x y. Discussion You must be signed in to discuss. Thus the dimensions of the desired box are 5 inches by 20 inches by 20 inches.

To find the maximumminimum volume we will use the lagranges multiplier method. Therefore λyz however x cant also be equal bc a cube violates the constraints. Find the maximum and minimum volumes of a rectangular box whose surface area equals 9000 square cm and whose edge length sum of lengths of all edges is 520 cm.

Solved Find the maximum and minimum volumes of a rectangular box whose surface area equals 8000 square cm and whose edge length sum of lengths of all edges is 480 cm. Surface area of the rectangular box is so And the total edge length is so The volume of the rectangular box is given by Chapter 148 Problem 44E is solved. Let be the length breadth and height of the rectangle.

Jump To Question Problem 44 Hard Difficulty Find the maximum and minimum volumes of a rectangular box whose surface area is 1500 c m 2 and whose total edge length is 200 c m. 0 t 2 π maximum value_____ minimum value_____ b f x y x 2 y 2. Use Lagrangemultipliers the surface area of an open rectangular box is the same as the surface area of a closed rectangular box.

Because the length and width equal 30 2 h a height of 5 inches gives a length and width of 30 2 5 or 20 inches.

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