Need help on 2 optimization problems

In summary, the first conversation is about finding the dimensions of a printed page with minimum area, given margins and printed area. The second conversation is about using calculus to solve for the length of the ladder needed to reach the exterior wall of a building over a 2m wide and 3m high corridor. The conversation also suggests drawing a picture to better understand the problem.
  • #1
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Question #1
A printed page will have margins of 2 cm at the top and sides and 4 cm at the bottom. If the printed area is 150cm squared, find the dimentions of the whole page so that its area will be a minimum.

Question #2
Painters are painting the second floor exterior wall of the building that adjoins a busy sidewalk. A corridor 2m wide and 3 m high is built to protect pedestrians. What is the length of the shortest ladder that will reach from the ground over the corridor of the wall of the building?
 
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  • #2
Ooh! Someone please answer this one. I have the same problems only with different numbers.
 
  • #3
i request to use calculus. take length as x-6. then solve for breadth dor he equation. report if you don't get after two days.
 
  • #4
Have you done ANYTHING except just copy the problem down?

1) Since you are asked for the dimensions of the page, let x= length, y= width of the page. What are the dimensions of the printed area?

2) Draw a picture! Draw the corridor, seen from the end, as rectangle and draw the ladder just touching the outer corner. Do you see that the ladder forms the hypotenuse of a right triangle?
 

1. What is optimization?

Optimization is the process of finding the best possible solution to a problem, given a set of constraints. It involves maximizing or minimizing a specific objective function by varying the input parameters.

2. How is optimization used in science?

Optimization is used in various scientific fields, such as engineering, economics, and physics, to find the most efficient and effective solutions to complex problems. It is also commonly used in data analysis and modeling to improve processes and systems.

3. What are the steps involved in optimization?

The basic steps in optimization include defining the problem, identifying the constraints, formulating an objective function, finding the optimal solution, and evaluating the results. This process may involve mathematical modeling, computer simulations, and statistical analysis.

4. What are the different types of optimization?

There are several types of optimization, including linear, nonlinear, dynamic, and stochastic optimization. Linear optimization involves optimizing linear objective functions with linear constraints, while nonlinear optimization deals with nonlinear functions and constraints. Dynamic optimization involves optimizing over a period of time, and stochastic optimization involves dealing with uncertain or random variables.

5. How is optimization different from other problem-solving methods?

Optimization differs from other problem-solving methods in that it focuses on finding the best possible solution, rather than just a satisfactory one. It also involves using mathematical and computational techniques to systematically search for the optimal solution, which may not be possible with other problem-solving methods.

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