Optimization Problem

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  • 1. Steph Garver Taylor Joyce Madison Klinghoffer Gabe Long Lena Sabih Megan Watson Optimization Problem
  • 2. Problem to Solve
    • Little Tommy Chaney is standing at point (7,0) away from a curving river. The river curves at the rate of y=0.5x ². What is the closest point on the river from where Tommy is standing?
  • 3. 1. Equation
    • y=0.5x ²
  • 4. 2. Graph the Equation Window= [-1,10] by [-1,10]
  • 5. 3. Put Point and Tommy on Graph Window= [-1,10] by [-1,10] Anywhere on line Tommy is at (7,0)
  • 6. 4. Put Triangle on Graph Window= [-1,10] by [-1,10]
  • 7. 5. Label Sides of Triangle Window= [-1,10] by [-1,10] y x 7-x D
  • 8. 6. Solve for D Window= [-1,10] by [-1,10] y x 7-x D Using Pythagorean Theorem… D= y ²+(7-x) ²
  • 9. 7. Put 0.5x ² in for y Window= [-1,10] by [-1,10] y x 7-x D Using Pythagorean Theorem… D= y ²+(7-x) ² D= (0.5x²)²+(7-x)²
  • 10. 8. Put D= (0.5x²)²+(7-x)² in Calculator
  • 11. 9. Find Minimum (2.13,5.37)
  • 12. 10. Go back to original equation to find y
    • Minimum- (2.13,5.37)
    • x= 2.13
    • Original Equation- y=0.5 x²…
    • y= 0.5(2.13)²
    • y= 2.27
    • (2.13, 2.27)
  • 13. 11. State the Final Answer
    • The closest point on the river from where Tommy is standing is (2.13, 2.27)
  • 14. Music from Title Page
    • Teenage Wasteland by the Who