Quantitative Analysis for

Quantitative Analysis for

Quantitative Analysis for Management: 8-15Margaret Black’s family owns five parcels of farmland broken into a southeast sector, north sector, northwest sector, west sector, and southwest sector.  Margaret is involved primarily in growing wheat, alfalfa, and barley crops and is currently preparing her production plan for next year.  The Pennsylvania Water Authority has just announced its yearly water allotment, with the Black farm receiving 7,400 acre-feet.  Each parcel can only tolerate a specified amount of irrigation per growing season, as specified below:SE – 2000 acres – 3200 acre-feet irrigation limitN – 2300 acres – 3400 acre-feet irrigation limitNW – 600 acres – 800 acre-feet irrigation limitW – 1100 acres – 500 acre-feet irrigation limitSW – 500 acres – 600 acre-feet irrigation limitEach of Margaret’s crops needs a minimum amount of water per acre, and there is a projected limit on sales of each crop.  Crop data follows:Wheat – 110,000 bushels (Maximum sales) – 1.6 acre-feet water needed per acreAlfalfa – 1800 tons (Maximum sales) – 2.9 acre-feet water needed per acreBarley – 2200 tons (Maximum sales) – 3.5 acre-feet water needed per acreMargaret’s best estimate is that she can sell wheat 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. Use Excel Solver(a) Formulate Margaret’s production plan.(b) What should the crop plan be, and what profit will it yield?(c) The Water Authority informs Margaret that for a special fee of $6000 this year, her farm will qualify for an additional allotment of 600 acre-feet of water.  How should she respond?

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