SOLUTION: The area of a certain rectangular pen is given by the formula: A(w) = 14w - w^2 ... where w represents the width in feet. a) Determine the width that produces the maximum area. b)

Question 1030987: The area of a certain rectangular pen is given by the formula: A(w) = 14w - w^2 ... where w represents the width in feet. a) Determine the width that produces the maximum area. b) What is the length of the pen (find the area with your answer to part a)? c) Of all rectangles, which particular type gives the maximum area?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The area of a certain rectangular pen is given by the formula:
A(w) = 14w - w^2 ... where w represents the width in feet.
a) Determine the width that produces the maximum area.
It's the vertex of the parabola.
A(w) = 14w - w^2
The vertex is on the Axis of Symmetry, w = -b/2a
w = -14/-2 = 7
A(7) = 98 - 49 = 49 sq feet
b) What is the length of the pen (find the area with your answer to part a)?
A(7) = 98 - 49 = 49 sq feet
L = 7 feet, w = 7 feet
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c) Of all rectangles, which particular type gives the maximum area?
A square (for a given perimeter).
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