Thread: Urgent Optimization Questions

Yes, I got 2 more problems....I really need some solutions to these...

1) You're desgning a rectangle poster to contain 50 in squared of printing with a 4-inch margin at the top and bottom and a 2-inch margin at each side. What overall dimensions will minimize the amount of paper used?

2) Two sides of a trianglehave lengths A and B, and the angle between them is theta. What value of theta will maximize the triang;e's area? Hint: A=1/2ABSinTheta

I'm in calculus and I do not know how to solve these problems. Any help is appreciated!

Originally Posted by Super Mallow

...

1) You're desgning a rectangle poster to contain 50 in squared of printing with a 4-inch margin at the top and bottom and a 2-inch margin at each side. What overall dimensions will minimize the amount of paper used?

...

Hello,

let x be the width and y the length of the printing area. Then the size of the poster is:



You know that . Plug in these values into the equation of A:

. You get the extreme (minimum or maximum) value if the 1st derivative of A equals zero:

. Solve the equation

for x. I've got . Use this value to calculate y. I've got

And now you can calculate the length and the width of the complete poster.

Originally Posted by Super Mallow

...

2) Two sides of a trianglehave lengths A and B, and the angle between them is theta. What value of theta will maximize the triang;e's area? Hint: A=1/2ABSinTheta

Hi,

take the equation of the function:



You'll get the extreme value if :



Solve for . I've got

Huge thanks man! I still don't get the first one..the answer in the book is 9x18, I don't see how to get tht answer!

I got that x=5. that makes y=10. When you plug that into the min area equation, you'll get (5+4)(10+8) which will give you your min dimensions.

And yes, I know this post is moldy oldy, but it may help the few people who use the search function...