Need help on 2 optimization problems

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Homework Help Overview

The discussion revolves around two optimization problems: one concerning the dimensions of a printed page with specific margin constraints and a fixed printed area, and the other regarding the length of a ladder needed to reach a wall over a corridor designed for pedestrian safety.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationships between the dimensions of the printed page and the area constraints. There is a suggestion to use calculus for the first problem, while the second problem prompts a geometric interpretation involving right triangles.

Discussion Status

Some participants have offered guidance on how to approach the problems, including suggestions to define variables and visualize the scenarios. There is an indication of varying levels of engagement, with some participants questioning the effort put into understanding the problems.

Contextual Notes

One participant notes that they have a similar problem with different numbers, which may influence the discussion dynamics. There is also a mention of a two-day timeframe for reporting progress on the problems.

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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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Ooh! Someone please answer this one. I have the same problems only with different numbers.
 
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.
 
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?
 

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