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Ans! 2018 June [] (b) The management of SAB Ltd. has suggested that a jear programming model might be used for selecting the best mix of five - A, B, C, D and E. The following information are possible products available. Per Unit of Product A B D E Sell Var Cor Let pro Ob Su 96 84 76 62 54 Selling price ): Costs (3): Material Direct Labour 30 28 32 30 32 a 36 32 12 8 8 b 18 16 6 4 4 Fixed Overhead 84 76 50 42 44 Total Costs Expected maximum unit demand per week for each product at the prices indicated: A B D E 3,000 2,400 1,800 1,200 1,200 Cost of material includes a special component which is in short supply. It costs 76 per unit. Only 11,600 units are available to the company during the week. The number of units of the special component needed for a unit of each product is: A B D E I 1 2 1 4 3 The management of SAB Ltd. has ruled that ure on materials must not exceed a sum of 60,000. All other resources are freely available in sufficient quantities for planned e need. Formulate a linear programming model stating clearly the criterion you use. (6 marks) 2017 - Dec [7] (b) A company produces products P, Q and R from three raw materials A, B and C. One unit of product P requires 2 units of A and 3 units of B. One unit of product Q requires 2 units of B and 5 units of C and one unit of product R requires 3 units of A, 2 units of B and 4 units of C. The company has 8 units of material A, 10 units of B and 15 units of C available to it. Profits per unit of product P, Q and Rare 3,5 and 4 respectively. (0) Formulate the problem mathematically. (ii) Write the Dual problem. (4+4 = 8 marks) 2013 - June [2] (a) A company manufactures two items X, and X2. They are sold at a profit of 7 30 per unit of X, and * 20 per unit of X. X, requires 2 kgs of materials, 3 man hours and 1 machine hour per unit. Xy requires 1 kg of material, 2 man hours and 3 machine hours per unit. During each production run there are 280 kgs of material available, 500 labour hours and 420 hours of machines used. Please introduce the slack variables and write down the equations, including the objective function, that will determine the quantity of production of the two items to maximize profits. (4 marke ative mited olex 2015 - June [3] {C} (i) What is the Simplex Method? State its advantage over the Graphical Method. (1 + 4 = 5 marks) as the keep ear ks) 2009-June [2] (b) A company manufactures items X, and X, which are sold at a profit of ? 35 per unit of X, and * 25 per unit of X. X, requires 3 kgs of materials, 4 man-hours and 2 machine-hours per unit. X, requires 2 kgs of materials, 3 man-hours and 2 machine-hours per unit. During each production run, there are 350 kgs, of materials available, 600 man-hours and 550 machine-hours for use. Formulate under Simplex method of linear programming: (i) the objective function and the linear constraints, and (ii) the equations after introducing slack variables. (iii) What are the various methods of solving a linear programming. problem? (2 + 2 + 2 = 6 marks) ng: et or 2016 - June [8] (b) Write the practical uses (three in each case) of Linear Programming in industrial and adminint Ansuar