Using previously found values we can easily calculate

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Using previously found values, we can easily calculate: The quantity of cow, buffalo and skimmed milk needed (as was illustrated earlier in detail  using alligations).  The sales in litres of bottled and loose milk. (bottling ratio * quantity) Bottling costs (bottling cost/litre found earlier * bottled sales) Skimmed milk costs (skimmed milk cost/litre * total skimmed milk needed) Sales revenues (using the costs given in the last column of Exhibit 3) Total Contribution  (Revenues – Bottling Costs – Skimmed Milk Costs). Other costs are  assumed to be irrelevant. The objective function then would be to maximize the total contribution, subject to the following  constraints: Total cow and buffalo milk used must be less than the procured fresh milk ( Table 1). 0 <= A,B,D <= 1
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C = 0 Solving the problem using the Simplex LP Solver in Excel, we get: A=1, B=1, C=0, D=1. This  suggests that MD should probably be selling all its milk in bottled form. The formulation is  present is the Excel workbook provided as a supplement. As an extract of the results, consider the total contribution figure for the two bottling ratio  scenarios summarized in the tables below: (Use “Zoom” if figures are too small… duh!) Table 4 Produce  (‘000  litres) Bottling  Ratio Bottled  Sales  (‘000  litres) Loose  Sales  (‘000  litres) Bottling Cost Skimmed  Milk Costs Total Contribution  (1962-63) Total  Contributio n (1961- 62) Whole  Milk 3,627 0.2857 1,036 2,590 29,950.31 0.00 2,768,175.41 2,581,633. 69 Toned  Milk 2,458 0.2857 702 1,755 20,296.06 274,446.87 1,601,428.50 849,982.7 8 Double  Toned 892.3 0 0 892.3 0.00 141,141.58 0.00 0.00 Cow  Milk 42.4 0.2857 12 30.285 350.10 1,446.55 30,911.92 6,198.78 Total 7,019 1,750 5,269.5 9 50,596.47 417,035 4,400,515.83 3,437,815. 25 Table 5 Produce  (‘000  litres) Bottling  Ratio Bottled  Sales  (‘000 litres) Loose  Sales  (‘000  litres) Bottling  Cost Skimmed  Milk Costs Total  Contribution  (1962-63) Total  Contributio n (1961- 62) Whole  Milk 3,627 1 3,627 0 104,826.08 0.00 2,796,933.92 2,688,117.9 2 Toned  Milk 2,458 1 2,458 0 71,036.20 274,446.87 1,620,916.93 957,256.9 3 Double  Toned 892.3 0 0.00 892.3 0.00 141,141.58 0.00 0.00 Cow  Milk 42.4 1 42.4 0 1,225.36 1,446.55 31,248.09 25,312.09 Total 7,019 6,127 892.3 177,087.64 417,035 4,449,098.94 3,670,686. 94 As can be seen, higher margins are obtained by using the new bottling ratios. Case 5B. This case has been introduced earlier. The only changes from the last case are as follows: The quantities – A, B, C, and D – of whole, toned, double toned, and cow milk to be made  and sold respectively are decision variables.
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The bottling ratios are fixed at 1,1,0,1 for the 4 products respectively. ( Note by a self- proclaimed mathematician in our group:  a non-linear approach was tried by keeping  these ratios also as decision variables. However, since Excel’s Simplex LP solver fails to  converge in that case, the GRG Non-Linear solver was tried. However, the found solutions  were  local rather than global  in nature. This was concluded from the fact that the GRG 
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  • Spring '12
  • AbhinavDhar
  • Ratio, MD

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