Optimization Problem

Steph Garver Taylor Joyce Madison Klinghoffer Gabe Long Lena Sabih Megan Watson Optimization Problem

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?

2. Graph the Equation Window= [-1,10] by [-1,10]

3. Put Point and Tommy on Graph Window= [-1,10] by [-1,10] Anywhere on line Tommy is at (7,0)

4. Put Triangle on Graph Window= [-1,10] by [-1,10]

5. Label Sides of Triangle Window= [-1,10] by [-1,10] y x 7-x D

6. Solve for D Window= [-1,10] by [-1,10] y x 7-x D Using Pythagorean Theorem… D= y ²+(7-x) ²

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

8. Put D= (0.5x²)²+(7-x)² in Calculator

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)

11. State the Final Answer The closest point on the river from where Tommy is standing is (2.13, 2.27)

Music from Title Page Teenage Wasteland by the Who

Optimization Problem

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Optimization Problem