I honestly have no clue how to do this problem
this is a maximum problem right?
i dont even know where to start, the wording is confusing
The strenghth of a wooden beam with a rectangular cross section and fixed length is proportional to the product of its width and the square of its height where the proportionailty constant is 2 psi.
Suppose the roofing company wants to make wooden beams of fixed length with rectangular cross sections from logs that are 4 inches in diameter. If the height of each beam must be at least 3.5 inches find the dimesnsions of the strongest beams.
Start by drawing a picture. You can take the cross section of a log to be the circle around the origin with radius 2: . The rectangular cross section of a beam made from that log will be a rectangle with vertices at (x,y), (-x,y), (-x,-y), and (x, -y) where x and y satisfy . Now, if "w" is the width of the rectangle, x= w/2 so and the height of the rectangle is .
Since "The strenghth of a wooden beam with a rectangular cross section and fixed length is proportional to the product of its width and the square of its height where the proportionailty constant is 2 psi", strength= .
Differentiate that with respect to w to find the value of w that maximizes that.