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Lesson 6-2: Problem-Solving Strategies

Scenario: Travel Optimization - Learn systematic approaches to tackle complex problems and make optimal decisions!

Duration: 75-90 minutesScenario: Travel Optimization

Learning Objectives

  • Apply systematic problem-solving approaches
  • Use optimization strategies to find best solutions
  • Make informed decisions using mathematical reasoning
  • Develop critical thinking and analysis skills

Travel Optimization Problem

Family Vacation Planning

Your family is planning a 5-day vacation with a budget of $1,200. You need to optimize your spending across different categories to maximize your experience while staying within budget.

Budget Categories:
• Accommodation: $80 per night
• Food: $40 per day per person (4 people)
• Activities: $25 per person per day
• Transportation: $200 total
• Souvenirs: Remaining budget
• What's the maximum you can spend on souvenirs?

Hotel

Food

Activities

Transport

Souvenirs

Budget categories

Systematic Problem-Solving Approach

Step 1: Identify and organize information

Total budget: $1,200
Duration: 5 days
People: 4 family members
Fixed cost: Transportation = $200

Step 2: Calculate daily variable costs

Accommodation per day: $80
Food per day: $40 × 4 people = $160
Activities per day: $25 × 4 people = $100
Total daily cost: $80 + $160 + $100 = $340

Step 3: Calculate total fixed and variable costs

Transportation: $200
Daily costs for 5 days: $340 × 5 = $1,700
Total committed costs: $200 + $1,700 = $1,900

Step 4: Identify the problem and find solution

Problem: $1,900 > $1,200 budget!
Need to reduce costs by: $1,900 - $1,200 = $700
Solution: Adjust daily spending or reduce days

Analysis: The current plan exceeds the budget by $700. You need to either reduce the number of days, find cheaper options, or increase the budget to make this vacation work.

Advanced Problem-Solving Strategies

1. Systematic Analysis

  • • Break complex problems into parts
  • • Identify all variables and constraints
  • • Organize information systematically
  • • Use tables or diagrams to visualize

2. Optimization Thinking

  • • Define what you want to maximize/minimize
  • • Consider all possible solutions
  • • Compare alternatives systematically
  • • Choose the best option

3. Constraint Analysis

  • • Identify limitations and boundaries
  • • Work within given constraints
  • • Find creative solutions within limits
  • • Adjust plans when constraints change

4. Decision Making

  • • Weigh pros and cons of each option
  • • Consider short-term and long-term effects
  • • Use mathematical reasoning to support decisions
  • • Be prepared to justify your choices

Real-World Applications

Travel & Logistics

  • • Route optimization
  • • Budget planning
  • • Time management
  • • Resource allocation

Business & Finance

  • • Cost-benefit analysis
  • • Investment decisions
  • • Resource optimization
  • • Risk assessment

Personal Life

  • • Time management
  • • Goal setting
  • • Problem resolution
  • • Decision making

Practice Problems

Problem 1

A school needs to transport 150 students on a field trip. Buses can carry 40 students each and cost $200 per trip. Vans can carry 8 students each and cost $50 per trip. What's the most cost-effective way to transport all students?

Your solution:

Problem 2

You have $500 to buy gifts for your family. You want to buy 3 items: a book ($25), a game ($45), and a toy ($30). You also want to buy some small items that cost $5 each. How many small items can you buy?

Your solution: