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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