## anonymous 4 years ago Optimization Problem: Ronnie is designing a poster to contain 50in^2 of printing with margins of 4 inches each at the top and at the bottom and margins of 2 inches at each side. What overall dimensions will minimize the amount of paper used?

1. kropot72

Let printing width = w and let printing length = x x * w = 50 w = 50/x Overall area A = (w + 4)(x + 8) Sustituting for w gives: A = (50/x + 4)(x + 8) Multiplying out gives: A = 4x + 400/x + 82 We need to find the value of x that makes A a minimum. Are you following so far?

2. anonymous

yeah, thanks

3. anonymous

wait, are you sure you got the multiplication right for A? i got something else

4. anonymous

just kidding, i did somethign wrong here

5. kropot72

Gr8. To find the value of x to give the minimum value of A we differentiate A with respect to x: dA/dx = 4 - 400/x^2 Now put the result equal to zero and solve for x: 4 - 400/x^2 = 0 x^2 = -400/-4 = 100 $x=\sqrt{100}=10$

6. anonymous

that is the correct answer, thank you sir

7. anonymous

my problem is i can't figure out the relevant equation to derive etc.

8. kropot72

So the optimum printing length is 10 inches. The optimum printing width is found from: x * w = 50 10 * w = 50 w = 5 So the optimum overall dimensions will be: Length = (10 + 8) = 18 inches Width = (5 + 4) = 9 inches

9. anonymous

could you do another one for me? or just part of it, i have it figured out but the arithmetic was crazy, i had to use wolfram, maybe there was another simpler way?

10. kropot72

Do you follow the method to get the overall dimensions?

11. anonymous

actually it's just 5" x 10"

12. anonymous

we included the area of the print in the overall dimensions

13. anonymous

A = (w + 4)((50/w) + 8) that's print area + margins = overall area

14. kropot72

Sorry for error. You are right. Good work :)