Question

The area of a planned garden can be modeled by the equation A = - 4w^2 + 64w,
where w is the width of the garden in feet.
Part A
What is the width, in feet, that will result in the maximum area?
Part B
What is the maximum area in square feet?

Answer 1

A = -4w^2 + 64w is a downward-opening parabola. The vertex gives the maximum:

w = -b/(2a) = -64/(2·-4) = 8 feet.

Maximum area: A(8) = -4(8)^2 + 64(8) = -256 + 512 = 256 square feet.

Answer — Part A: 8 ft. Part B: 256 ft².