An agriculturist has a 125-acre farm. He produces radish, Carrot and potato. Whatever he raises is fully sold in the market. He get $5 for radish per kg, $4 for carrot per kg and $5 for potato per kg. The average per acre yield is 1500kg of radish, 1800 kg of carrot and 1200 kg of potato. To produce each 100 kg of radish and carrot and 80 kg of potato, a sum of $12.5 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 carrot. A total of 500 man-days of labor at a rate of $40 per man-day are available. Formulate this as a linear programming model and solve by simplex method to maximize the agriculturist’s total profit.
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