I want to replicate a linear programming problem.I have the following information, for the background." A fuzzy regression analysis with only one independent variable X results in the following bivariate regression model: $$ \hat{Y}=\tilde{A_o}+\tilde{A_1}X,$$
where $\tilde{A_o}$ is a is a fuzzy intercept, $\tilde{A_1}$is a fuzzy slope coefficient, the parameters are expressed as $\tilde{A_i}=(m_i,c_i)$ where $m_i$ is a centre and $c_i$ is the fuzzy half-width."
To determine the fuzzy coefficients the following linear programming problem is used:
minimize $$ S= nc_0 + c_1\sum_{i=1}^{n}|X_i|$$
subject to $$c_0\geqslant0,\geqslant0,$$
$$\sum_{j=0}^{l}m_iX_{ij}+(1-h)\sum_{j=0}^{l}c_i|X_{ij}| \geqslant Y_i+(1-h), \mbox{for i=1 to n}$$
$$\sum_{j=0}^{l}m_iX_{ij}-(1-h)\sum_{j=0}^{l}c_i|X_{ij}| \geqslant Y_i-(1-h), \mbox{for i=1 to n}$$
where $h=0$
I have the following data : $[X_i : Y_i]=[(2:14),(4:16),(6:14),(8:18),(10:18),(12:22),(14:18), (16:22)]$
Q1:how to write this down, for a novice?
Q2:how to solve using R?
I want to learn.
Thank YOU!