A cell phone manufacturer wishes to make a rectangular phone with fixed total surface area of 12, 000 mm2 that will have maximal screen area. The screen is surrounded by bezels on all sides with sizes of dh mm on the height and dw mm on the the width. (So, for example, the width of the screen would be the width of the phone minus 2 dw mm.) The following figure shows an illustration with adjustable values for dw and dh. The screen area varies as the the point P (w,h) is moved along the constraint.

Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter8: Areas Of Polygons And Circles
Section8.4: Cicumference And Area Of A Cicle
Problem 13E
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A cell phone manufacturer wishes to make a rectangular phone with fixed
total surface area of 12, 000 mm2 that will have maximal screen area.
The screen is surrounded by bezels on all sides with sizes of dh mm on the
height and dw mm on the the width. (So, for example, the width of the
screen would be the width of the phone minus 2 dw mm.)
The following figure shows an illustration with adjustable values for dw and
dh. The screen area varies as the the point P (w,h) is moved along the
constraint.
JSXGraph y12 Copyright (C) see https://jsxgraph.org
800
height
700
600
500
dh = 32.00
dw = 8.00
400
screen area = 5700
P=(w,h)
300
200
100
O + +
Suppose the bezels have sizes 4 mm on the width (dw) and 15 mm on the
height (dh).
Transcribed Image Text:A cell phone manufacturer wishes to make a rectangular phone with fixed total surface area of 12, 000 mm2 that will have maximal screen area. The screen is surrounded by bezels on all sides with sizes of dh mm on the height and dw mm on the the width. (So, for example, the width of the screen would be the width of the phone minus 2 dw mm.) The following figure shows an illustration with adjustable values for dw and dh. The screen area varies as the the point P (w,h) is moved along the constraint. JSXGraph y12 Copyright (C) see https://jsxgraph.org 800 height 700 600 500 dh = 32.00 dw = 8.00 400 screen area = 5700 P=(w,h) 300 200 100 O + + Suppose the bezels have sizes 4 mm on the width (dw) and 15 mm on the height (dh).
200
100
50
100
150
-100
TC
1.
Suppose the bezels have sizes 4 mm on the width (duw) and 15 mm on the U
height (dh).
(a) What is the height of the phone?
Tt
(b) What is the width of the phone?
(c) The dimensions for most phones have a height that is about twice the
width. Is that the case for your answer?
No the height to width ratio is closer to 1 to 1
Yes, the height to width ratio is basically 2 to 1
No, the height to width ratio is closer to 3 or more to 1•
(d) Show your work used to compute w and h.
8 +E
Transcribed Image Text:200 100 50 100 150 -100 TC 1. Suppose the bezels have sizes 4 mm on the width (duw) and 15 mm on the U height (dh). (a) What is the height of the phone? Tt (b) What is the width of the phone? (c) The dimensions for most phones have a height that is about twice the width. Is that the case for your answer? No the height to width ratio is closer to 1 to 1 Yes, the height to width ratio is basically 2 to 1 No, the height to width ratio is closer to 3 or more to 1• (d) Show your work used to compute w and h. 8 +E
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