Given the following dual pair of LP problems

a) Introduce surplus (slack) variables in the primal and dual inequality constraints and give them a meaningful economic interpretation. Write down the corresponding equations. Choose symbol XS for the surplus variable of the primal constraint and choose symbol YS for the surplus variable of the dual constraint.

b) Show that these surplus variables are always nonnegative.

c) State the primal and the dual complementary slackness conditions using the surplus variables.

d) Complete and explain these statements in economic terms:

Primal max TR sub ect to DS Dual min TC sub ect to MC > MR