Question 9 (AGRICULTURAL PRODUCTION PLANNING) Margaret Kowalchuk's family owns five parcels of farmland broken into a southeast sector, north sector, northwest sector, west sector, and southwest sector. Kowalchuk 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 Kowalchuk farm receiving 7400 acre-feet. Each parcel can only tolerate a certain amount of irrigation per growing season, as specified in the following table: WATER IRRIGATION LIMIT (ACRE-FEET) PARCEL AREA (ACRES) Southeast North Northwest West Southwest 2000 2300 600 1100 500 3200 3400 800 500 600 1 Each of Kowalchuk's crops needs a minimum amount of water per acre, and there is a projected limit on sales of each crop. Crop data follow: WATER NEEDED PER ACRE (ACRE-FEET) CROP MAXIMUM SALES Wheat Alfalfa Barley 110 000 bushels 1 800 tons 2 200 tons 1.6 2.9 3.5 Kowalchuk'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. (a) Formulate Kowalchuk's production plan. (b) What should the crop plan be, and what profit will it yield? Use Solver to create the Answer and Sensitivity Reports for this LP problem. Now answer the following questions using these reports. Each question is independent of the others. (a) (b) (C) (d) Is this solution a unique optimal solution? Why or why not? If there are alternative solutions, use Solver to identify at least one other optimal solution Would it help Margaret's total profit if she could increase barley sales by 10%. If so, how? How would the availability of more water affect Margaret's total profit