The optimizing function of the printed area is while dimensions that maximize the printed area is 80 by 12 cm
Assume the dimensions of the poster be w and h, where:
w represents the width.
h represents the height.
So, the area of the poster is:
a= hw
The area is given as 960.
So, we have:
hw = 960
w = 960/h
When the height is reduced by 10 cm and the width by 6 cm.
The printed area (P) becomes
p =(w-12)(h-20)
p =(960/h-12)(h-20)
p = (960-12h/h)(h-20)
p =960h - 19200-12h²+240h
p = -12h²+1200h-19200
p = 80,20
w = 960/h
w = 960/80 = 12
Consequently, 80 by 12 cm are the dimensions that maximize the printed area.
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