# Optimization and Closest Point on a Line

1. Minimize the perimeter of rectangles with area 25 cm^2 . Is there a maximum perimeter of rectangles with area 25 cm?

2. Find two numbers whose difference is 100 and whose product is a minimum.

3. If 1200 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

4. Find the point on the line 6x+y=9 that is closest to the point (-3,1)(Check your answer with the grapher)

5. Maximize the area of rectangles inscribed in the right triangle with lengths of sides 5, 12, and 13.

https://brainmass.com/math/optimization/optimization-closest-point-line-152525

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Find the point on the line that is closest to the point (Check your answer with the grapher) ...

#### Solution Summary

This solution looks and optimization and investigates how to calculate the closest point on a line. This solution is provided in two attached Word documents.