4. Consider the following linear program. ():maxs.t.3x4y+z+3w5xz+3w2xy+2wxyzw670000 (a) (1 point) Write down the dual of the above linear program (without converting it to the standard form). (b) (1 point) By plotting the boundaries defined by the dual of (), show that the dual program is infeasible. (c) (1 point) Provide a justification that () is feasible without solving the linear program. (d) (1 point) Explain why the duality theorem is not violated in this example