- #1

Mathman2013

- 23

- 1

- Homework Statement
- Optimization problem (Max area of a combined semi circle and a square)

- Relevant Equations
- f (w) = (4 - 9/7*w)*w + 11/28*w^2

A figure is made from a semi circle and square. With the following dimensions, width = w, and length = l.

Find the maximum area when the combined perimiter is 8 meter.

I first try to construct the a function for the perimeter.

2*l + w + 22/7*w/2 = 8 - > l = 4 - (9*w)/7

Next I insert this into a function which is suppose to define the area.

f(w) = l*w + 1/2*22/7*(w/2)^2 and substitute l with l = 4 - (9*w)/7

which results in f(w) = (4 - 9/7*w)*w + 11/28*w^2

I find the derivative of this function f'(w) = -(25*w)/14 + 4 and solve f'(w) = 0 and find that w is suppose to be 2.24 m

However the solution manual says w = 1.86 m.

So what am I doing wrong?

Find the maximum area when the combined perimiter is 8 meter.

I first try to construct the a function for the perimeter.

2*l + w + 22/7*w/2 = 8 - > l = 4 - (9*w)/7

Next I insert this into a function which is suppose to define the area.

f(w) = l*w + 1/2*22/7*(w/2)^2 and substitute l with l = 4 - (9*w)/7

which results in f(w) = (4 - 9/7*w)*w + 11/28*w^2

I find the derivative of this function f'(w) = -(25*w)/14 + 4 and solve f'(w) = 0 and find that w is suppose to be 2.24 m

However the solution manual says w = 1.86 m.

So what am I doing wrong?