1. Geophysicists are mapping the earth underneath to recover the hydrocarbon. Using the sound reflection data, they develop the model for trapped hydrocarbon as z(x,y) = (2 y2 + x3)(1-z- A SXSB,C SY SD, and E SzSF where x,y and z are in kilometers. a. Describe the geometry of the model and identify the possible critical point(s) for the trapped hydrocarbon. Justify your solutions. b. Assume the volume of hydrocarbon in the reservoir will reduce by 10% after 1000 years. Identify the best constant values for G, H,), and K subjected to the earth model in the time domain below: x(t) = Get and y(t) = Jekt Evaluate the rate of change at the coordinate in Part 1(a) and the direction in which the reduction occurs. C. Based on your answers in Part 1(a) and Part 1(b), identify the maximum rate of change that will give the smallest value for A,B,C,D,E and F. Calculate the volume of hydrocarbon (50 marks)