Applications of Calculus. (1 Viewer)

[RivalryofTroll]

A printed page of a book is to have side margins of 1cm, top margin of 2cm and a bottom margin of 3cm.

It is to contain 200cm^2 of printed matter. Find the dimensions of the page if the area of paper used is to be a minimum.

Working so far:

A = (x+5)(y+2)
xy = 200
x = 200/y

A(y) = whatever
A'(y) = whatever
A'(y) = 0

Then I got y = root80. And showed that it was a minimum.

xy = 200
Therefore when y = root80 then x = 10root5.

A = b x h = (x+5)(y+2)

b = (x+5) = 10root5 + 5 = 5(2root5 + 1) [answer says 5(root5 +1)]
h = y + 2 = root80 + 2 = 4root5 + 2 = 2(2root 5 + 1) [this is correct according to answers)

What did I do wrong?

 

[Sy123]

A printed page of a book is to have side margins of 1cm, top margin of 2cm and a bottom margin of 3cm.

It is to contain 200cm^2 of printed matter. Find the dimensions of the page if the area of paper used is to be a minimum.

Working so far:

A = (x+5)(y+2)
xy = 200
x = 200/y

A(y) = whatever
A'(y) = whatever
A'(y) = 0

Then I got y = root80. And showed that it was a minimum.

xy = 200
Therefore when y = root80 then x = 10root5.

A = b x h = (x+5)(y+2)

b = (x+5) = 10root5 + 5 = 5(2root5 + 1) [answer says 5(root5 +1)]
h = y + 2 = root80 + 2 = 4root5 + 2 = 2(2root 5 + 1) [this is correct according to answers)

What did I do wrong?

Look at their answers, what do they imply?

That their own x is



Lets multiply to check if it meets 200





(I did it and you are correct)