Calculus optimization question

Question

1. Find the maximum area of a rectangle inscribed in the region bounded by the graph of y= 4-x / 2+x  and the coordinate axes.[8 marks]
2. Two isolated farms are situated 10 km apart on a straight road. The road runs parallel to a highway that is 20 km away. A power company decides to run a wire from the highway to a junction box, and from there, it will run two separate wires of equal length to the two farms. Find the distance from the highway that the junction box should be placed to minimize the length of the wire needed? [8 marks]

Answer 1

y=4-x/2+x

Area = xy = (4-x)x/(2+x)

take the derivative, set = 0, solve for x, then for y

xy would then = maximum area

that's a general method, which might work

calculations look complicated though