A box of volume 216 m³ with a square bottom and no top is made of two different materials. The cost of the bottom is $40/m²and the cost of the sides is $30/m². Find the dimensions of the box that minimize the total cost.(Use symbolic notation and fractions where needed. Write the objective function with respect to the length of thesquare bottom.)length of the bottom side:height of the box:mm A box (with no top) is to be constructed from a piece of cardboard of sides A and B by cutting out squares with sides of length hfrom the corners and folding up the sides.A figure shows a rectangle of width A and height B. All four corners of the rectangle have dotted squares of side h.Suppose that the box height is h = 3 in, and that it is constructed using 138 in² of cardboard (i.e. AB = 138). What values Aand B maximize the volume?(Use decimal notation. Give your answer to three decimal places. Give your answer in the form of a comma-separated list.)A, B =in

Let The length of the bottom side = x height = y volume = 216 x·x·y=216 y=216x2

A box of volume 216 m³ with a square bottom and no top is made of two different materials. The cost of the bottom is $40/m² and the cost of the sides is $30/m². Find the dimensions of the box that minimize the total cost. (Use symbolic notation and fractions where needed. Write the objective function with respect to the length of the square bottom.) length of the bottom side: m

A box of volume 216 m³ with a square bottom and no top is made of two different materials. The cost of the bottom is $40/m² and the cost of the sides is $30/m². Find the dimensions of the box that minimize the total cost. (Use symbolic notation and fractions where needed. Write the objective function with respect to the length of the square bottom.) length of the bottom side: m

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.1: Prisms, Area And Volume

Problem 40E: As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in....

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