Production Planning & Scheduling Problem (Agriculture)

*Problem and Answers Below*
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(Agriculture production planning problem)

Margaret Black's family owns five parcels of farmland borken 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 planning 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:

Parcel Area (acres) Water Irr Limit (acre-ft)
SE 2,000 3,200
N 2,300 3,400
NW 600 800
W 1,100 500
SW 500 600

Each 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 follow:

Crop Max Sales Water / Acre Net Profit Yield/Acre
Wheat 110,000 bushels 1.6 $2.00 50 bushels
Alfalfa 1,800 tons 2.9 $40.00 1.5 tons
Barley 2,200 tons 3.5 $50.00 2.2 tons

Margaret's best estimate is that she can sell wheat at a net profit of $2/bushel, alfalfa at $40/ton, and barley at $50/ton. One acre of land yields an average of 50 bushels of wheat, 1.5 tons of alfalfa, and 2.2 tons of barley.

SOLVE:
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 $6,000 this year, her farm will qualify for an additional allotment of 600 acre-feet of water. How should she respond?

ANSWERS:
1,250 wheat in N parcel, 500 wheat in NW, 312.5 in W, 137.5 wheat in SW, 131 alfalfa in SW, 600 barley in SE, 400 barley in N, profit = $337.862.10

*PLEASE TELL ME HOW THESE ANSWERS WERE DERIVED AT*
*PLEASE TELL ME HOW THESE ANSWERS WERE DERIVED AT*
*PLEASE TELL ME HOW THESE ANSWERS WERE DERIVED AT*