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a) Find a formula for the height of the printed area (h) in terms of its width (w). b) Show that the total area (A) of the entire notice board (including the margins) is given by: 8000 A = 820 + 20w +9 W c) Find the dimensions of the entire board (including the margins), which minimizes the quantity of board required. d) Check that these dimensions indeed give a minimum value as opposed to a maximum. h W

a) Find a formula for the height of the printed area (h) in terms of its width (w). b) Show that the total area (A) of the entire notice board (including the margins) is given by: 8000 A = 820 + 20w +9 W c) Find the dimensions of the entire board (including the margins), which minimizes the quantity of board required. d) Check that these dimensions indeed give a minimum value as opposed to a maximum. h W

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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12. A notice printed on water-proof board is required, on which the rectangular area allowed for the message (shown shaded) is to be 500 cm². The top and bottom margins are to be 10 cm wide and the side margins are to be 8 cm wide. a) Find a formula for the height of the printed area (h) in terms of its width (w). b) Show that the total area (A) of the entire notice board (including the margins) is given by: 8000 A = 820 + 20w + W c) Find the dimensions of the entire board (including the margins), which minimizes the quantity of board required. d) Check that these dimensions indeed give a minimum value as opposed to a maximum. h
Transcribed Image Text:12. A notice printed on water-proof board is required, on which the rectangular area allowed for the message (shown shaded) is to be 500 cm². The top and bottom margins are to be 10 cm wide and the side margins are to be 8 cm wide. a) Find a formula for the height of the printed area (h) in terms of its width (w). b) Show that the total area (A) of the entire notice board (including the margins) is given by: 8000 A = 820 + 20w + W c) Find the dimensions of the entire board (including the margins), which minimizes the quantity of board required. d) Check that these dimensions indeed give a minimum value as opposed to a maximum. h
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optimisation has to be used   answer for width is 36 and height is 45 cms

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