Question

Q1: A company has four factories F1, F2, F3, and F4 manufacturing the same product. Production and raw material costs differ from factory to factory and are given in the following table in the first two rows. The transportation costs from the factories to the sales depots, S1, S2, and S3 are also given. The last two columns in the table give the sales price and the total requirement at each depot. The production capacity of each factory is given in the last row. F1 F2 F3 F4 Sales price per Requirement unit 1518 14 13 109129 Production cost/unit Raw material cost/unit Transportation cost/unit S1395434 S2174532 S3 5 8 3 6 80 120 150 Supply T 50 150 50 100 Determine the most profitable production and distribution schedule and the corresponding profit. The deficit production should be taken to yield zero profit.

Answer 1

Particulars F1 F2 F3 F4 Requirement Sales per unit Production cost/ unit 15 14 13 Raw Material cost/ unit 10 9 12 Transportation cost/ unit S1 3 9 5 4 80 1 7 4 120 5 8 3 6 150 Supply 50 150 50 100 Since only the minimization problem can be solved using the transportation problem, the total cost has to be minimized. 52 S3 S1 36 26 Calculation of Total Cost: Total Cost = Production cost - Raw Material cost Transportation cost Particulars FIT F2 F3 F4 Requirement 31 S2 34 S3 Supply 150 100 350 / 350 Requirement = Supply, therefore it is a balanced problem. Being a balanced problem, the problem can be proceeded for Vogel Method. 26 28

Particulars F1 F2 F3 F4 Requirement Iteration 1 Iteration 2 Iteration 3 Iteration 4 80 26 80/0 50 20 27 120/70/50/0 la 100 28|150 / 100 / 0 50/0 150 50/0 100/20/0 350 / 350 Supply Iteration 1 Iteration 2 Iteration 3 Iteration 4 No. of Allocated Cells = Order of Matrix -1 = 4+3 -1 = 6 Since both are equal, the solution is optimal.

Profit Matrix and allocated cells Particulars F1 F2 F3 F4 SP 50 S3 100 - 4 50 Profit Units Product 640 Cell Allocated S1F4 S2F1 S2F2 50 -100 100 -400 100 640 S3F3 Profit