Answer the following questions: Problem1. A patient consult a doctor to check up his ill health. Doctor examines him and advises him that he is having deficiency of two vitamins, vitamin A and vitamin D. Doctor advises him to consume vitamin A and D regularly for a period of time so that he can regain his health. Doctor prescribes tonic X and tonic Y, which are having vitamin A, and D in certain proportion. Also advises the patient to consume at least 40 units of vitamin A and 50 units of vitamin daily. The cost of tonics X and Y and the proportion of vitamin A and D that present in X and Y are given in the table below. Vitamins A D Cost in birr per unit X 2 3 5 Tonic Y 4 2 3 Daily requirements in units 40 50 a) Formulate L.P.P. to minimize the cost of tonics. b) Solve by using Graphical method and simplex method. c) Justify your answer by comparing two methods solution. Problem2. Four factories, A, B, C and D produce sugar and the capacity of each factory is given below: Factory A produces 10 tons of sugar and B produces 8 tons of sugar, C produces 5 tons of sugar and that of D is 6 tons of sugar. The sugar has demand in three markets X, Y and Z. The demand of market X is 7 tons, that of market Y is 12 tons and the demand of market Z is 4 tons. The following matrix gives the transportation cost of 1 ton of sugar from each factory to the destinations.
