[10 points] Suppose you ran an experiment and obtained the data in the table below. The theory behind the experiment suggests that the data values should satisfy an equation of the form Yi = co + c Xi + c2 xi2 + c3 sin(xi) + e; for some values of co, C1, C2, and c3 and e; is the measurement error (the measurement error is unknown). Find a nonlinear programming model designed to minimize the Euclidean norm of the vector of measurement errors [e1, ..., e8] subject to the constraint that each measurement error is at most 10% of the absolute value of the corresponding y value. You do not need to find the solution to the model. [Note: I made up the data values in the table so the resulting model may not have a feasible solution.] 1 1 10.4 2 2 12.6 3 4 20.3 | 4 | 5 | 14.5 5 6 8.9 6 8 5.2 710 1.3 8 | 12 -2.7 [10 points] Suppose you ran an experiment and obtained the data in the table below. The theory behind the experiment suggests that the data values should satisfy an equation of the form Yi = co + c Xi + c2 xi2 + c3 sin(xi) + e; for some values of co, C1, C2, and c3 and e; is the measurement error (the measurement error is unknown). Find a nonlinear programming model designed to minimize the Euclidean norm of the vector of measurement errors [e1, ..., e8] subject to the constraint that each measurement error is at most 10% of the absolute value of the corresponding y value. You do not need to find the solution to the model. [Note: I made up the data values in the table so the resulting model may not have a feasible solution.] 1 1 10.4 2 2 12.6 3 4 20.3 | 4 | 5 | 14.5 5 6 8.9 6 8 5.2 710 1.3 8 | 12 -2.7