Sample Midterm1_Solution

Sample Midterm1_Solution - ∑ ∑ ∑ = = = + + 5 1 5 1 5...

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Problem #1 X1= 4, X2 = 2 (intersection of constraint 2 with constraint 3) Z = 18 Problem #2: Solution: will be posted on Thursday Feb. 9 by 11:00 p.m. (check the solution to assignment #3: SensitivityAssSolution.doc) Problem # 3: P.S: this is the formulation of 3-12, given on HMW 1 Let Xi,j _ acres of crop i planted on parcel j where i =1 for wheat, 2 for alfalfa, 3 for barley and j = 1 to 5 for SE, N, NW, W, and SW parcels Max Z = = = = + + 5 1 5 1 5 1 3 ) 2 . 2 ( 50 $ 2 ) 5 . 1 ( 40 $ 1 ) 50 ( 2 $ j j j j X tons j X tons j X bushels Subject to Irrigation limits: 1.6 X 11 + 2.9 X 21 + 3.5 X 31 <= 3,200 acre-feet in SE 1.6 X 12 + 2.9 X 22 +3.5 X 32 <=3,400 acre-feet in N 1.6 X 13 + 2.9 X 23 + 3.5 X 33 <=800 acre-feet in NW 1.6 X 14 + 2.9 X 24 +3.5 X 34 <= 500 acre-feet in W 1.6 X 15 + 2.9 X 25 + 3.5 X 35 <= 600 acre-feet in SW
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Unformatted text preview: ∑ ∑ ∑ = = = + + 5 1 5 1 5 1 3 5 . 3 2 9 . 2 1 6 . 1 j j j j X j X j X <= 7,400 water acre-feet total Sales limits: X 11 + X 12 + X 13 + X 14 + X 15 <= 2,200 wheat in acres (=110,000 bushels) X 21+ X 22 + X 23 + X 24 + X 25 <= 1,200 alfalfa in acres (= 1,800 tons) X 31+ X 32 + X 33 + X 34 + X 35 <= 1,000 barley in acres (= 2,200 tons) Acreage availability: X 11 + X 21 + X 31 <= 2,000 acres in SE parcel X 12 + X 22 + X 32 <= 2,300 acres in N parcel X 13 + X 23 + X 33 <= 600 acres in NW parcel X 14 + X 24 + X 34 <= 1,100 acres in W parcel X 15 + X 25 + X 35 <= 500 acres in SW parcel All Xij >= 0 i= 1, 2, 3 and j= 1, 2, 3, 4...
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This note was uploaded on 09/27/2008 for the course ADM 2302 taught by Professor El during the Fall '05 term at University of Ottawa.

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Sample Midterm1_Solution - ∑ ∑ ∑ = = = + + 5 1 5 1 5...

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