(b) The architect then considers the shape where the semi-circle doesn't reach the full width of the rectangle, though is still centred. Set up this problem that is similar to that of part (a) but with an extra variable. The want to maximise the area becomes more subtle as with the option to vary the size of the semi-circle now included, this means could have a semi-circle of radius 0. In other words, the option to not remove any semi-circle at all is included in the problem, and this would indeed maximise the area of the window. The architect still decides to do some investigating with the area S and the imposition of the xed contour only. Here the architect nds that there is a local maximum to maybe consider. Find this local maximum area along with associated measurements, prove its nature and discuss its feasibility in terms of the other constraints. Working may be done with exact values or with numbers correct to four decimal places. Any nal measurements should be given correct to two decimal places. Area of the window A = xxh - 5( T ( 2)2) A = xh -1 Tx A = Xh - T x2 8 where , boundary conditions 1) Azo ii ) x 20 iii ) h >o iv ) The length of the boundary of shape = 600 0m 2 x + 1 + 1/2TT ( X/2) ) = 600 2xth+ Trn = 600 2