question_answer 1)

There are two types of fertilizers F1 and F2¬, F1 consists of 10% nitrogen and 6% phosphoric acid and F2 consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, a fearmer finds that the needs at least 14kg. f nitrogen and 14kg. Of phosphoric acid for her crop. If F1¬ costs Rs. 6 kg and F2costs Rs.5/kg, determine how much of each type of fertilizer should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost ? 

Answer:

Let x kg of fertilizer I and y kg of fertilizer II and used. The contents of fertilizer and given below :             Therefore, the above L.P.P. is given as              Minimum cost, C = 6x + 5y, subject to the constraints,             i.e. 2x + y       L1 : 2x + y = 280      L2 : 3x + 5y = 700                                                                               Here cost is minimum at E (100, 80) and is Rs.100       Since the region is unbounded, thereforeRs.1000 may or not may not be the minimum value of C. For this draw graph of inequality.             L : 6x + 5y = 1000             Clearly open half plane has no common point with the feasible region so minimum value of C = Rs.1000.