Please solve the following Operational research problem. Please show all work for this problem

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2. A corporation has decided to produce four new products. Five branch plants now have excess production capacity. The unit manufacturing cost of the first product would be $28, $24, $30, and $27 in plants A, B, C, and E, respectively, whereas, plant D does not have the capability for producing this product. The unit manufacturing cost of the second product would be $29, $33, $28, $32, and $31 in plants A, B, C, D, and E, respectively. The unit manufacturing cost of the third product would be $39. S32, $28, and $31 in plants A, B, D, and E, respectively, whereas, plant C does not have the capability for producing this product. The unit manufacturing cost of the fourth product would be $30, $26, $25, $32, and $31 in plants A, B, C, D, and E, respectively. Sales forecasts indicate that 500, 300, 200, and 400 units of products 1, 2, 3, and 4, respectively, should be produced per day. Plant A, B, C, D, and E have the capacity to produce 300, 400, 200, 500, and 300 units daily, respectively, regardless of the product or combination of products involved. Management wishes to know how they should allocate the new products to plants in order to minimize total manufacturing cost. a) Formulate this problem as a transportation problem by constructing the appropriate cost and requirements table. [10 points) Product Product 2 Product 3 Product 4 Supply Plant A Plant B Plant C Plant D Plant E Demand b) Use the northwest-corner method to obtain an initial basic feasible solution for the problem. 5 points) Product Product 2 Product 3 Product 4 Plant A Plant B Plant C Plant D Plant E c) Use the minimum-cost method to obtain an initial bfs for the problem. [5 points) Product Product 2 Product 3 Product 4 Plant A Plant B Plant C Plant D Plant E d) Use the Vogel's method to obtain an initial basic feasible solution for the problem. [5 points) Product Product 2 Product 3 Product 4 Plant A Plant B Plant C Plant D Plant E e) Using Transportation Simplex method to obtain the next iteration of part (d). [15 points)