A family farming concern owns five parcels of farmland broken into a southeast 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.€ƒ
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.

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.

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?

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WATER IRRIGATION AREA LIMIT (ACREF PARCEL (ACRES Southeast 2,000 North Northwest 600 West Southwest 500 3,200 3,400 800 500 600 2.300 1,100 MAXIMUM WATER NEEDED PER CROP SALES ACRE (Ac-EET) 1.6 2.9 Wheat 110,000 bushels Alfalfa 1,800 tons Barley 2,200 tons 3.5