I don't understand how to solve optimization problems, (like here's the volume of a box, find the least amount of material it would take to make such a box).
Is there a tutorial or some general step by step instruction on how to do these?
Thanks in advance,
Amy :)
http://mathdemos.gcsu.edu/mathdemos/maxmin/maxmin.html
Additionaly, I highly recommend the work book Schaum's Outline Series, Calculus, available at your college bookstore, or Barnes Noble. Go look at it. It is very inexpensive.
Hi Amy! Optimization problems can be a bit tricky, but with practice and understanding of the steps involved, they can become easier to solve. Here's a general step-by-step guide to solve optimization problems:
1. Understand the problem: Read the problem carefully and identify what you are trying to optimize. In your example, you mentioned finding the least amount of material to make a box.
2. Identify the variables: Determine the variables involved in the problem and assign them letters. For this box problem, you might have variables for the length, width, and height of the box.
3. Formulate the objective function: Create an equation that represents the quantity you want to optimize. In this case, you are minimizing the amount of material, so the objective function could be the total surface area of the box.
4. Write down any constraints: Constraints are conditions or limitations that you need to consider when solving the problem. For a box, there may be constraints on its volume or proportions.
5. Express the objective function in terms of a single variable: Eliminate any variables that are not necessary in the objective function by using the constraints or other equations given in the problem.
6. Find the critical points: Differentiate the objective function with respect to the remaining variable(s) and find the critical points by setting the derivative equal to zero. These critical points correspond to potential maximum or minimum values.
7. Check for endpoints and boundaries: Consider any constraints that involve inequality signs, such as a minimum or maximum value for a variable. Check if these boundaries could also be potential solutions.
8. Evaluate the critical points and endpoints: Plug the critical points and endpoints into the objective function to find the corresponding values. Compare them to determine the minimum or maximum value.
9. Check the feasibility: Ensure that the solution you found satisfies all the constraints given in the problem. Sometimes, additional steps may be needed to verify feasibility.
10. Interpret the results: Lastly, interpret the solution in the context of the problem. For a box optimization problem, you would describe the dimensions of the box that would minimize the amount of material needed.
For additional guidance, you can also refer to the tutorial you mentioned (http://mathdemos.gcsu.edu/mathdemos/maxmin/maxmin.html) as it provides visual examples and explanations. Additionally, using resources like the Schaum's Outline Series, Calculus workbook can be a helpful supplement for practice and deeper understanding.
I hope this explanation helps you with solving optimization problems! Feel free to ask if you have any further questions.