1 When a manufacturer makes x items per day, the cost function is C(x) = 720 + 4x + 0.02x2 dollars and the price function is p(x) = 15 0.0023 dollars per item. Find the production level that will maximise profits. 2 A duck farmer wishes to build a rectangular enclosure of area 100 m2. 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 shorter sides have length x m, show that the required length of wire netting to be purchased 100 is L= 2x + 100 b Use technology to help you sketch the graph of y= 2x + c Find the minimum value of L and the corresponding value of x when this occurs. d Sketch the optimum situation showing all dimensions