Book about optimization problems

In summary, the conversation was about finding a book or resource to help with understanding and solving optimization problems for a Calculus 1, 2, 3 final exam. The recommendation was to use the techniques covered in a Calculus textbook or start with online resources like the one provided. The weight limit of 40 grams and the variables of paper, wire, and fixture were discussed in relation to maximizing the light surface area.
  • #1
hi guys, i am preparing my self for the calculus 1 2 3 final and i need recommendation about optimization problems theories book or something to help me understand how to solve and understand optimization problems and to solve them. Thanks♥
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  • #2
Can you be more specific? Are you referring to like minimum or maximum problems? How many variables? What book(s) are you using for Calculus?
  • #3
Yes like for example
Each tree is made by iron wire structure a translucent paper cone open at the bottom. The metallic structure of the decoration is obtained
welding on the basic circumference two linear pieces corresponding to two apotems of the cone.
The weight of the paper used is p1 = 25g = m2, and each conical cover is obtained from a sheet
35 cm square on the side. The weight of the wire is instead equal to p2 = 0; 08g = cm, while
the electric apparatus (lamp holder, bulb and cable) and the bill hook weigh 30 g per
each decoration.
Each suspension point of the support can bear a maximum weight of 40 g.
The single tree is tantopièu decorative, how much greater is the luminous surface (therefore the
base does not count).
Determine the optimal measures of decoration

[Translated from other language]
  • #4
So you have a limitof 40 grams. This is a constraint. You have some items (paper wire and fixture) add up to make total weight. You need to create an expression which represents the weight in some variables. It looks like you want to maximize the light surface area? Create an expression for surface area. Use Calculus to find a maximum. See if that fits into the constraints. The amount of paper is also constrained.
  • #5
So any recommendation about any kind of book that teach that stuff ? :) or resource/s
Please i would really appreciate it! :-p

1. What is the definition of optimization problems?

Optimization problems are mathematical problems that involve finding the maximum or minimum value of a function, subject to certain constraints. These problems arise in various fields, such as engineering, economics, and computer science.

2. What are the different types of optimization problems?

The most common types of optimization problems are linear programming, quadratic programming, integer programming, and nonlinear programming. Each type has its own set of techniques and algorithms for solving them.

3. What are some real-world applications of optimization problems?

Optimization problems have many real-world applications, including production planning, resource allocation, portfolio optimization, and logistics management. They are also widely used in machine learning and artificial intelligence algorithms.

4. How do you formulate an optimization problem?

To formulate an optimization problem, you need to define the objective function, which represents the quantity you want to maximize or minimize. You also need to specify the constraints, which are the limitations or conditions that the solution must satisfy. Finally, you need to identify the decision variables, which are the values that can be adjusted to optimize the objective function.

5. What are some common techniques for solving optimization problems?

There are several techniques for solving optimization problems, such as the simplex method, branch and bound, genetic algorithms, and gradient descent. The choice of technique depends on the type of problem and its specific characteristics, such as the size of the problem and the number of constraints.

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