Solve this linear program in AMPL. Record the input file along with the feasible solution and objective

value. For this question, you can hard code the parameters in your model file and no data file is

necessary.

$2.$ Derive the dual LP$.$ Then write down the dual linear program in AMPL. Record the input file along

with the feasible solution and objective value. For this question, you can hard code the parameters in

your model file and no data file is necessary.

$3.$ Verify by hand calculation that AMPL$$s solution to the primal problem is indeed optimal. Justify your

answer by leveraging concepts from duality $($without using the Simplex method$).$

i got the same optimal value for the primal LP and dual LP$.$ is that natural? does that make sense? and how do i solve #$3?$