A duck farmer wishes to build a rectangular enclosure of area 100 m. The farmer must purchase wire netting for three of the sides, as the fourth side is an existing fence. Naturally, the farmer wishes to minimise the length (and therefore cost) of fencing required to complete the job. a If the sides adjacent to the existing fence have length x m, show that the required length of wire netting to be 100 purchased is L = 2x + X CONDITIONS OF EMPLOYMENT m b Find the minimum value of L and the corresponding value of x when this occurs. c Sketch the optimal situation, showing all dimensions.