It is assumed that there is a connection between X and Y variables in the form $Y=a{x}^3+bx+c$ and that the sum of the coefficients $a,b$ and c $,$ which cannot take negative values in this connection, is $1.$ Write the linear programming problem that can perform the necessary operations to calculate the coefficients $a,b$ and c in such a way as to minimize the sum of the absolute values of the errors between the measurements listed below and the predictions to be calculated with the formula above.