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. 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 mat11(a) Write an equation for the volume of the box.81 =9w? h813wh281 =w2 h81 =3w2 h81 == 9wh?(b) Write an equation for the cost of the box in terms of w and h.C = 24wh + 18w²C = 12wh + 4w2C = 24wh + 6w²Oc = 12wh + 6w2C = 24wh + 12w²Oc = 6wh + 2w2(c) Write an equation for the cost in terms of w only. Use lower case w.C(w)(d) Find C '(w)%3D(e) Find the dimensions that minimize the cost of the box.W =inchesh =inches

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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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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.

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
11
(a) Write an equation for the volume of the box.
81 =
9w? h
81
3wh2
81 =
w2 h
81 =
3w2 h
81 =
= 9wh?
(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
Oc = 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)
%3D
(e) Find the dimensions that minimize the cost of the box.
W =
inches
h =
inches

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