A rectangular sheet of paper has the area $24$ sq. meters. The bottom is $75$ cm and sides $50$ cm each. What are the dimensions of the printed space is maximum.

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Solution

Printed area is = $24 - 0.75 x - 0.50 y$ where $x, y$ are the length and breadth of the sheet.
Also, $x y = 24$
$24 - 0.75 x - \frac{12}{x}$
$- 0.75 + \frac{12}{x^{2}} = 0$
$x^{2} = 16$
$x = 4, y = 6$
Printed area = $24 - 3 - 3 = 18$ sq.meters

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A rectangular sheet of paper has the area 24 sq. meters. The bottom is 75cm and sides 50cm each. What are the dimensions of the printed space is maximum.

Printed area is =24−0.75x−0.50y where x,y are the length and breadth of the sheet.Also, xy=2424−0.75x−12x−0.75+12x2=0x2=16x=4,y=6Printed area = 24−3−3=18 sq.meters

A rectangular sheet of paper has the area $24$ sq. meters. The bottom is $75$ cm and sides $50$ cm each. What are the dimensions of the printed space is maximum.

Printed area is = $24 - 0.75 x - 0.50 y$ where $x, y$ are the length and breadth of the sheet.
Also, $x y = 24$
$24 - 0.75 x - \frac{12}{x}$
$- 0.75 + \frac{12}{x^{2}} = 0$
$x^{2} = 16$
$x = 4, y = 6$
Printed area = $24 - 3 - 3 = 18$ sq.meters