Write down a linear programming problem

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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!