Assignment 2 Question 7 Farmer Leary 1 Farmer

Assignment 2 Question 7 Farmer Leary 1

Farmer Leary • Farmer Leander grows wheat and corn on his 45 -acre farm in Saskatoon. He can sell at most 140 bushels of wheat and 120 bushels of corn. Each planted acre yields either 5 bushels of wheat or 4 bushels of corn. Wheat sells for $30 per bushel, and corn sells for $50 per bushel. Six hours of labour are needed to harvest an acre of wheat, and ten hours are needed to harvest an acre of corn. Up to 350 hours of labour can be purchased at $10 per hour. Let – A 1 = acres planted with wheat – A 2 = acres planted with corn – L = hours of labour that are purchased • Farmer Leander maximizes his profits by solving the LP problem stated in the LINDO output below. • Answer the following questions according to this LINDO output (do not resolve it each time). Justify your answers for each. 2

Farmer Leary SUBJECT TO 2) 3) 4) 5) 6) END MAX RANGES IN WHICH THE BASIS IS UNCHANGED: 150 A 1 + 200 A 2 - 10 L OBJ COEFFICIENT RANGES CURRENT ALLOWABLE COEF INCREASE A 1 150. 000000 10. 000000 A 2 200. 000000 50. 000000 L -10. 000000 INFINITY A 1 + A 2 <= 45 6 A 1 + 10 A 2 - L <= 0 L <= 350 5 A 1 <= 140 4 A 2 <= 120 LP OPTIMUM FOUND AT STEP VARIABLE 1 ROW OBJECTIVE FUNCTION VALUE 1) VARIABLE VALUE A 1 25. 000000 A 2 20. 000000 L 350. 000000 ROW 2) 3) 4) 5) 6) 2 3 4 5 6 4250. 000 SLACK OR SURPLUS 0. 000000 15. 000000 40. 000000 REDUCED COST 0. 000000 RIGHTHAND SIDE RANGES CURRENT ALLOWABLE RHS INCREASE 45. 000000 1. 200000 0. 000000 40. 000000 350. 000000 40. 000000 140. 000000 INFINITY 120. 000000 INFINITY ALLOWABLE DECREASE 30. 000000 10. 000000 2. 500000 ALLOWABLE DECREASE 6. 666667 12. 000000 15. 000000 40. 000000 DUAL PRICES 75. 000000 12. 500000 0. 000000 3