How to linearize the following LP

Question

I want to minimize $|d_1-d_2|+e1+e2+e3$ where $d_1,d_2,e_1,e_2,e_3>=0$ and $|.|$ denotes the absolute value, for some linear constraints. Is there any way I can linearize the objective function?

Answer 1

Is this homework? If you have the problem

min $|d_1-d_2|+e_1+e_2+e_3$

with the constraints $d_1,d_2,e_1,e_2,e_3\geq0$

then by introducing a new variable $\lambda$ with $\lambda\geq d_1-d_2\geq -\lambda$ we have the following LP whos optimum is just the same as the above

min $\lambda+e_1+e_2+e_3$

with the constraints $\lambda - d_1 + d_2\geq 0$, $\lambda + d_1 - d_2\geq 0$ and $\lambda,d_1,d_2,e_1,e_2,e_3\geq0$