You are designing a rectangular poster to contain 7575 in2 of printing with a 33-in margin at the top and bottom and a 11-in margin at each side. What overall dimensions will minimize the amount of paper used?

The dimensions of the rectangular poster is 15 in by 5 in.

Step-by-step explanation:

Given that, the area of the rectangular poster is 75 in².

Let the length of the rectangular poster be x and the width of the rectangular poster be y.

The area of the poster = xy in².

....(1)

1 in margin at each sides and 3 in margin at top and bottom.

Then the length of printing space is= (x-2.3) in

                                                           =(x-6) in

The width of printing space is = (y-2.1) in

                                                  =(y-2) in

The area of the printing space is A =(x-6)(y-2) in²

∴ A =(x-6)(y-2)

Putting the value of y

Differentiating with respect to x

Again differentiating with respect to x

To find the minimum area of printing space, we set A' = 0

Now putting x=±15 in A''

Since at x=15 , A"<0 Therefore at x=15 , the area will be minimize.

From (1) we get

Putting the value of x

   =5 in

The dimensions of the rectangular poster is 15 in by 5 in.

a)(x-2)^2+(y-1)^2=9

step-by-step explanation:

(picture explains)

step-by-step explanation: