- Please include any assumptions made and the full working steps for both the questions, thank you!

1. Construct a function of two variables to represent water tank surface that is continuous on an interval and has absolute maximum and minimum values. Find the area of the surface with minimal height of the flat bottom water tank that gives volume of 1000 m. If the top and bottom of the water tank are not flat, propose a set of function that gives total volume of 1005 m3 with minimal height, absolute maximum and minimum values. Verify the results and sketch the water tank. (50 Marks] 2. As a Production Executive at the Sunshine Bread factory your main task is to monitor the production of one of its machines. TABLE 2 represents number of hours spent at your factory with number of breads produced (in thousands) that could be produced by the machine (output) in one day. You are required to propose reasonable number of breads produced in thousands) for the given time spent. TABLE 2 Time spent (hours) 3 5 6 8 10 12 Number of bread (in thousands) Based on the data in TABLE 2, generate a suitable interpolating polynomial, f(x) of order more than 3. Using the polynomial obtained, estimate the number of breads produced by the machine for time equal to 11.5 hours (the answer must be rounded off to the nearest integer). Assume that the machine operates for 13 hours, plot a graph that depicts the polynomial and discuss the behavior of the machine. Estimate the rate of production by using the polynomial obtained when the production is at 7 hours by using a step size h = 2 hours with TWO (2) different numerical methods. Find the true percent relative error (&) in each estimate. Select the best numerical method and justify your answer. [50 marks]