Exercises 169 3-27. A family farming concern owns five parcels of farmland broken into a sou- theast sector, north sector, northwest sector, west sector, and southwest sector. The farm concern is involved primarily in growing wheat, alfalfa, and barley crops and is currently preparing the production plan for next year. The Water Authority has just announced its yearly water allotment, with this farm receiving 7,500 acre-feet. Each parcel can tolerate only a certain amount of irrigation per growing season, as specified in the following table. Parcel Area (acres) Water Irrigation Limit (acre-feet) Southeast North Northwest West Southwest 2,000 2.300 600 1,100 500 3,200 3,400 800 500 600 Each crop needs a minimum amount of water per acre, and there is a projected limit on sales of each crop, as noted in the following table. Crop Maximum Sales Water Needed per Acre (acre-feet) 1.6 Wheat Alfalfa Barley 110,000 bushels 1,800 tons 2,200 tons 2.9 3.5 Wheat can be sold at a net profit of $2 per bushel, alfalfa at $40 per ton, and barley at $50 per ton. One acre of land yields an average of 1.5 tons of alfalfa and 2.2 tons of barley. The wheat yield is approximately 50 bushels per acre. What is the best planting plan for this farm? 3-28. A farmer has subdivided his land into three plots and wants to plant three crops in each plot: corn, rice, and soy. Plot sizes, crop acreage, profit per acre, and manure needed (pounds per acre) are given in the table for this problem. Plot Acreage Crop Maximum Acreage Profit per Acre Manure per Acre (pounds) A B 500 800 700 Corn Wheat 900 700 $600 $450 $300 200 300 150 C Soy 1,000 The maximum acreage for each crop denotes the total acres of that crop that can be planted over all three plots. Currently there are 450,000 pounds of manure available. To ensure that the plots are used equitably, the farmer wants the same proportion of each plot to be under cultivation. (The propor- tion of each plot under cultivation must be the same for all three plots.) How much of each crop should be planted at each plot to maximize total profit