QUESTION ONE (a) The finished product of a company has a requirement that it must weigh atleast 150kg. The two raw materials used in the manutacture of this product are A with a cost of K4 per unit and B with cost of K16 per unit. Each unit of A weighs 10kg and each unit of B weighs 20kg. At least 28 units of B and no more than 40 units of A must be used. Determine how much of each type of raw material should be used for each unit of the finished product in order to minimize the cost. [6 marks] (a) Three products A,B,C are produced in three machine centres x,y, and z. Each product involves operation of each of the machine centres. The time required for each operation on various products is indicated in the following Table. 100, 77 and 80 hours are only available at machine centres x,y and z respectively. The profit per unit of A,B and C is K12,K3 and K1 respectively. (i) Construct the LPP that maximizes the protit. [4 marks] (ii) Solve the LPP in (i). [8 marks] (iii) Determine the dual problem to the LPP constructed in (i). [7 marks] [Total: 25 marks]