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Optimal Rectangular Field Dimensions Problem Solving

Explore how to find dimensions for a rectangular field with maximum area using calculus optimization principles, illustrated through an example from Todd Fadoir's Calculus Section 4.7 in CASA 2003.

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Optimal Rectangular Field Dimensions Problem Solving

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  1. Section 3.7Optimization Problems

  2. Example • Find two numbers whose difference is 100 and whose product is a minimum. Calculus, Section 4.7, Todd Fadoir, CASA, 2003

  3. Example Calculus, Section 4.7, Todd Fadoir, CASA, 2003

  4. Summary • Find relationship between unknown values • Write a function for the quantity needing to be maximized or minimized. • Reduce the function to one variable. • Take the first derivative of the function, and find value that maximizes or minimizes the quantity. • Answer the question posed. Calculus, Section 4.7, Todd Fadoir, CASA, 2003

  5. Example • A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. • He needs no fence along the river. • What are the dimensions of the field that has the largest area? What is the area? Calculus, Section 4.7, Todd Fadoir, CASA, 2003

  6. w h Calculus, Section 4.7, Todd Fadoir, CASA, 2003

  7. w h Calculus, Section 4.7, Todd Fadoir, CASA, 2003

  8. Assignment • Section 4.7, 1-17, odd Calculus, Section 4.7, Todd Fadoir, CASA, 2003

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