Q15 An agriculturist has a farm with 126 acres. He produces Radish, Muttar and Potato. Whatever he raises is fully sold in the market, he gets Rs.5 for radish per kg., Rs. 4 for Muttar per kg. and Rs. 5 for Potato per kg. the average yield is 1,500 kg. of Radish per acre, 1800 kg. of Matter per acre and 1200 kg. of Potato per acre. To produce each 100 kg. of Radish and Muttar and to produce each 80 Kg. of potato, a sum of Rs. 12.50 has to be used for manure. Labour required for each acre to raise the crop is 6 man-days for Radish and Potato each and 5 man-days for Muttar. A total of 500 man-days of labour a a rate of Rs. 40 per man day are available. Formulate this as a linear programming model to maximize the agriculturists total profit.
Ans: Maximize (Z) = 7072.5×1+6775×2+5572.5×3
Subject to constraints x1+x2+x3≤125, 6×1+5×2+6×3≤500,
Non Negative Restrictions x1, x2, x3≥0
