Monisha Black’s family owns five parcels of farmland, referred to as the southeast sector, north sector, northwest sector, west sector, and southwest sector. Monisha is involved primarily in growing wheat, alfalfa, and barley crops and is currently preparing the production plan for next year. The Pennsylvania Water Authority has just announced its yearly water allotment, with the Black farm receiving 7,400 acrefeet. Each parcel can tolerate only a specified amount of irrigation per growing season, as specified in the following table: 

Each of Monisha’s crops needs a minimum amount of water per acre, and there is a projected limit on sales of each crop. Crop data follow: 

Monisha’s best estimate is to 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 Monisha’s production plan. 

(b) What should the crop plan be, and what profit will it yield? 

(c) The Water Authority informs Monisha that for a special fee of $6,000 this year, the farm will qualify for an additional allotment of 600 acre-feet of water. How should Monisha respond?

Transcribed Image Text:

PARCEL Southeast North Northwest West Southwest AREA (ACRES) 2,000 2,300 600 1,100 500 WATER IRRIGATION LIMIT (ACRE-FEET) 3,200 3,400 800 500 600