# yeo.34. Find the dimensions that will minimize the surface area of a rectangular box with an open tophaving à volume of 32 cubic feet. Use the Method of Lagrange Multipliers.x2-33 o-32X2xy

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61 views help_outlineImage Transcriptioncloseye o.3 4. Find the dimensions that will minimize the surface area of a rectangular box with an open top having à volume of 32 cubic feet. Use the Method of Lagrange Multipliers. x2-33 o -32 X2 xy fullscreen
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Step 1

Let x be the height , y and z be the dimensions of base of rectangular box, then volume is length*breadth *height

and surface area is shown on board.

Step 2

Now, consider the function F as shown on board, we will partial derivative of F with respect to the variablex, y, z and lagrange multiplier and set them equal to zero.

Step 3

On solving first three equations simultaneou...

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### Derivative 