Last min/max problem I can't get my mind wrapped around :(

[PrincessOfSteel92]

A printed page is to have a 1 inch margin on the top and the bottom and a 3/4 inch margin on each side.
The printed is to be 44 inches

What are the dimensions of the page that minimizes the paper used?


No work started, damn thanksgiving turkey screwed up my train of thought lol.

please help me get started?

 

[galactus]

Re: Last min/max problem I can't get my mind wrapped around

Draw a picture. Label the print width x and the height y.

The area of the print is \(\displaystyle xy=44\)............[1]

Thus, the area of the whole page is \(\displaystyle A=(x+\frac{3}{2})(y+2)\).........[2]

Solve [1] for y and sub into [2]. Minimize.

 

[PrincessOfSteel92]

Re: Last min/max problem I can't get my mind wrapped around

Draw a picture. Label the print width x and the height y.

The area of the print is \(\displaystyle xy=44\)............[1]

Thus, the area of the whole page is \(\displaystyle A=(x+\frac{3}{2})(y+2)\).........[2]

Solve [1] for y and sub into [2]. Minimize.

X is solved with respect to y then I subbed in y.

Now minimize it how?

 

[galactus]

Re: Last min/max problem I can't get my mind wrapped around

Yep. It is now in terms of one variable. This is how most min/max problems are solved. Eliminating a variable.

\(\displaystyle A=(x+\frac{3}{2})(\frac{44}{x}+2)\)

Minimize by differentiating, setting to 0 and solving for x.

Remember, x is the width of the print. They are asking for the diemnsions of the whole page. Easy to get once you get x.