$2\mathrm{.}7.$ Consider a linear program with a single constraint

minimize,$z=c_1{x}_1+c_2{x}_2+$cdots$+c_n{x}_n$

subject $to{a}_1{x}_1+a_2{x}_2+$cdots$+a_n{x}_{n}b$

$,x_1,x_2,$dots,$x_{n}0.$

Using duality develop a simple rule to determine an optimal solution, if the latter

exists.