A farmer has 500 metres of fencing to construct a rectangular enclosure, plus two internal fences to divide the enclosure into three rectangular sections of equal area, as shown in the picture below. Following the steps below, you will find the dimensions of the enclosure and internal fences which will maximise the total area. a) Clearly define the variables you will use, including the units in which they are measured. b) Write down the relationship between the variables given by the constraint in the problem on the amount of materials available. c) Write down the objective function (which is the function to be optimized). d) Solve the optimization problem, including your intermediate steps. e) Write a sentence which puts your solution into the context of the problem. This will not involve the variables you have introduced in part (a), and must have sufficient information that the farmer can build the enclosure by following your instructions. () Write the total area enclosed in the solution you found in the box below