You are constructing a closed box whose length, I, is three times its width, w, as indicated in the labels on the figure below. The mat (a) Write an equation for the volume of the box. 81 = 9w2 h 81 = 3wh? 81 = w2 h 81 = 3w2 h 81 = 9wh2 (b) Write an equation for the cost of the box in terms of w and h. C = 24wh + 18w² C = 12wh + 4w2 C = 24wh + 6w2 C = 12wh + 6w2 C = 24wh + 12w² OC = 6wh + 2w2 (c) Write an equation for the cost in terms of w only. Use lower case w. C(w) = (d) Find C '(w) = (e) Find the dimensions that minimize the cost of the box. W = inches h = inches
You are constructing a closed box whose length, I, is three times its width, w, as indicated in the labels on the figure below. The mat (a) Write an equation for the volume of the box. 81 = 9w2 h 81 = 3wh? 81 = w2 h 81 = 3w2 h 81 = 9wh2 (b) Write an equation for the cost of the box in terms of w and h. C = 24wh + 18w² C = 12wh + 4w2 C = 24wh + 6w2 C = 12wh + 6w2 C = 24wh + 12w² OC = 6wh + 2w2 (c) Write an equation for the cost in terms of w only. Use lower case w. C(w) = (d) Find C '(w) = (e) Find the dimensions that minimize the cost of the box. W = inches h = inches
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter4: Polynomials
Section4.9: Area Problems
Problem 1P
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You are constructing a closed box whose length, l, is three times its width, w, as indicated in the labels on the figure below. The material costs $2 per square inch for the top and bottom and $3 per square inch for the sides. The box must hold 81 cubic inches.
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