Skip to content

Optimization Problem Setup Flowchart

Run the Optimization Flowchart MicroSim Fullscreen

Edit this MicroSim with the p5.js editor

About This MicroSim

This interactive flowchart guides you through the systematic process of setting up and solving optimization problems in calculus. The flowchart is color-coded into three sections:

  • Blue (Setup): Problem understanding and equation formulation
  • Green (Calculus): Applying calculus techniques
  • Orange (Verification): Confirming and stating results

How to Use

  1. Hover over any step to see a detailed explanation in the info panel
  2. Click on a step to see how that step applies to a sample problem (maximizing garden area)
  3. Walk Through Example button animates through all steps with a worked example

Embed This MicroSim

You can include this MicroSim on your website using the following iframe:

1
<iframe src="https://dmccreary.github.io/calculus/sims/optimization-flowchart/main.html" height="502px" width="100%" scrolling="no"></iframe>

The Ten Steps

Setup Phase (Blue)

  1. Read Problem - Identify whether you're maximizing or minimizing
  2. Draw Diagram - Sketch the situation and label all variables
  3. Write Objective Function - Create the equation for what you want to optimize
  4. Write Constraint Equation - Identify what quantity is fixed or given

Calculus Phase (Green)

  1. Reduce to Single Variable - Use the constraint to eliminate one variable
  2. Determine Practical Domain - Find what values make physical sense
  3. Find Critical Points - Set the derivative equal to zero and solve
  4. Decision: Closed Interval? - Determines which verification method to use

Verification Phase (Orange)

8a. Check Endpoints (if closed interval) - Compare values at critical points AND endpoints 8b. Use Derivative Test (if not closed) - Apply first or second derivative test

  1. State Final Answer - Give the answer in the context of the original problem with units

Sample Problem

Problem: A farmer wants to fence a rectangular garden against a wall. She has 100 feet of fencing. What dimensions maximize the area?

The animation walks through each step showing how to solve this classic optimization problem.

Lesson Plan

Learning Objectives

After using this MicroSim, students will be able to:

  1. Identify and execute the sequential steps for setting up optimization problems
  2. Distinguish between the setup, calculus, and verification phases
  3. Choose the appropriate method (closed interval vs. derivative test) based on the domain

Suggested Activities

Introduction (5 min)

  • Display the flowchart and briefly explain the three color-coded sections
  • Emphasize that optimization follows a systematic process

Guided Exploration (10 min)

  • Click "Walk Through Example" to show the garden problem
  • Pause at each step to discuss what's happening
  • Have students take notes on each step

Practice (15 min)

  • Give students a different optimization problem
  • Have them use the flowchart to guide their work
  • They can hover over steps for reminders

Assessment

  • Students should be able to list all steps from memory
  • Given a new problem, students can correctly identify what each step requires

Common Misconceptions

  • Forgetting to check endpoints on closed intervals
  • Not considering practical domain restrictions (negative lengths, etc.)
  • Giving answers without context or units

References