ICE CREAM PARLOUR LPP PROBLEM

Details :Amul parlor, near vanaz company, kothrud We visited to our nearest AMUL ice cream parlor shop which is near our residence consisting of 2 freezer of 500 liters each. There we collected information in 3 variant sizes as family pack, large cups equivalent to large cones and small cups similar to small cones. So here family pack we considered of 1 liter, large cups & cones of 60 ml and small cups & cones of 45 ml. Here for using linear programming we took profit as our objective function for maximizing profit and thus as per the discussion with parlor owner he said the profit is around 18% so by deducting electricity bill and freezer depreciation he remains with 12% of the profit so our decision variable will we 12% as our net profit of price. We have considered profit on per liter basis as family pack calculation is obtained easily but for large cup we obtained profit on 60 ml and then converted to per liter basis to keep all the denominations same for profit in liters. So based on the data collected we will find the objective function as How many numbers of boxes the parlor should sold to a particular flavor to earn the maximum profit

Objective: Profit maximizationDefine: Decision VariableX1 = quantity of vanilla flavor sold or stored with the size of 1 liter.X2 = quantity of chocolate flavor sold or stored with the size of 1 liter.X3 = quantity of rajbhog flavor sold or stored with the size of 1 liter.X4 = quantity of mango flavor sold or stored with the size of 1 liter.X5 = quantity of butter scotch flavor sold or stored with the size of 1 liter.X6 = quantity of green pista flavor sold or stored with the size of 1 liter.X7 = quantity of vanilla flavor sold or stored with the size of 60 ml.X8 = quantity of butter scotch flavor sold or stored with the size of 60 ml.X9 = quantity of vanilla flavor sold or stored with the size of 40 ml.X10 = quantity of butter scotch flavor sold or stored with the size of 40 ml.Objective Function:ZMax= 7.2X1 + 9.6X2 + 14.4X3 + 10.8X4 + 9X5 + 8.4X6 + 50X7 + 50X8 + 30X9 + 30X10Vanilla family pack profit = price*12%60*0.12 = 7.2It would be same for rest of 5 flavor as depending on price of ice cream flavor.Vanilla & butter scotch large cup& cones profit = price of (60 ml)*12%25*0.12 = 3So if profit on sale of 60 ml of cup gives 3 rs as profit so for 1 liter it would be 50 rs as this has to be done because we cannot compare family pack of 1 liter profits with 6o ml of large cups profit so we have calculated profit for large cups and small cups in denominations of 1 liter.Vanilla & butter scotch small cup & cones profit = price of (40 ml)*12%10*0.12 = 1.2For 40 ml profit is 1.2 rsso for 1 liter we would get profit as 30 rs.Under Constraints: Here we have compared data with the price as we cannot compare price which is mentioned in the table and the amount of liter we get in the solution so we have made constraints in price as price*units of demand.Vanilla family pack: