Consider Mr$.$ Meadows Cookie Company, described in Problem $24.$ Suppose that the cost of hiring workers each period is $$100$ for each worker until $20$ workers are hired, $$400$ for each worker when between $21$ and $50$ workers are hired, and $$700$ for each worker hired beyond $50.$

a$.$ Write down the complete linear programming formulation of the revised problem.

b$.$ Solve the revised problem for the optimal solution. What difference does the new hiring cost function make in the solution?$($Which is a continuation of the problem stated in part a$).$ Using the additional information stated, formulate the revised problem and state the changes from the formulation in part a$).$