min c'x

st. ax=b

x_1 = l_1

x_2 = l_2

x_1 >= sqrt(x_2^2 + x_3^2)

c and a are arbitrary 3 dimensional vectors. l_1 and l_2 are scalar constants.

The above problem is in fact a 1 dimensional LP. The exercise is:

- Write the 1 dimensional LP?
- State the corresponding dual problem.
- Show how to recover the dual solution to conic problem from the dual solution to the the LP.
- What if l_1 - |l_2| = 0? Does it give rise to problems?