Consider the following LP problem

min w $$ cTx $($Objective Function$)$

s$.$t$.$

aTx $$ b $($One Constraint$)$

x $0($Sign Restrictions$)$

where c$,$ a$,$ and x are all n $1$ and b is a scalar.

a$.)(10$ points$)$ Derive a simple test for checking the feasibility of this problem.

b$.)(10$ points$)$ Assuming that the optimal cost is finite, develop a simple method for

obtaining an optimal solution directly using c$,$ a and b$.$ You may assume for this part that

b $0.$