Linear Programming Techniques — DU B.A. (Prog.) with Statistics as Major Discipline Previous Year Question Papers

6. (a) (i) Write short notes on Slack and Surplus variables. (ii) Justify the statement `Graphical solution is Pot possible for LPP with more than two variables'. (b) Explain Hungarian method for solving assignment problem. (c) Give a brief outline of the procedure for solving transportation problem. (6,6,6) 2. Attempt five `questions in all. 1. Answer the following : (a) An optimal solution of an assignment problem can be .obtained if the number of assigned cells is to the number of rows/column. (1) (b) In a balanced transportation problem with in sources and n destinations, the number of non basic feasible variables are mE (c) Slack variables in a LPP convert a constraint into an equation when the con.stra.int is type. (d) Assignment problem is a special case of problem. (e) In a minimization problem of a simplex table, if there will be solution. (1) (D The cost coefficient of surplus variable in objective function is (g) Explain the graphical method of solving a LPP involving two variables. (3) demand of 5,15,15 and 15 truckloads respectively. The unit transportation cost per truckload on the different routes is given below : Solve the problem to get the optimal transportation schedule in order to maximize the transportation cost. (b) Find the initial basic feasible solution of the following transportation problem using north west comer method and least cost method. Also, compute the transportation cost on the basis of initial basic feasible solution and compare the results. FactoryJ Warehouse Warehouse requirement 5 (h) Explaifi transportation problem and show that it can be mathematically formulated as. an LPP. 4. (a) Solve the following LPP using Big-M method : subject to constraints: (b) Describe assignment problem an+d also, for.mulate it mathematically. A company wis.hes to assign 3 jobs to 3 machines in such a way that each job is assigned to some ,, machine and no machine works on more than one job. The cost of assigning job i to machine j is given by the following matrix : Cost matrix : Formulate the given problem as LPP. (9,9) 5. (a) A transport company ships truckloads of grains from three warehouses with supply capacity of 25, 2.5 an.d 10 truckload.s to four mills with the (i) Reduce the following LPP into its standard form Subject to the constraints : unrestricted in size. (3) 0.) Compute all the basic solutions to the following system of linear equations : 2. (a) A company that produces soft drinks has a contract that requires a minimum of 80 units of chemical A and 60 units of chemical 8 to go into each bottle of the drink. The chemicals are available in a prepared mix from two different suppliers. Supplier X[ has a mix of 4 unit of A and 2 units of 8 that costs Rs.10, and supplier X2 has a mix of 1 unit of A and 1 unit of 8 that costs. Rs.4. How many mixes from company X] and company X2 should the company purchase to honour contract requirements and yet minimize the cost? Formulate the problem as LPP and solve it graphically.