Let r=radius of the semicircle, so the width of the glass is 2r. Let length of the rectangular part be x. The perimeter is πr+2x+2r≤30m.
Area of the glass is A=πr²/2+2rx=πr²/2+r(30-πr-2r)=if the perimeter is 30m.
The derivative dA/dr=0=πr+30-2πr-4r=30-πr-4r at maximum or minimum.
Therefore, r=30/(π+4)=4.20m, and 2x=30-30(π+2)/(π+4)=60/(π+4)=8.40m.
Note that this means we have a square glass with a semicircular top, so x=r.
Area of the glass is 63.01m² approx, costing $614.36 approx.