ESE 403 Fall 2017MidtermDue 3:00PM Friday, October 131. (35pt)(a) (10pt)max 10b + 2f + 5rs.t. b + f + r + s1= 12b − s2= 2f − s3= 3b + f + s4= 8r , t , e , s1, s2, s3, s4≥ 0(b) (25pt) Phase 1Iter B.V. Z b f r s1s2s3s4a2a3RHS Ratio0aZ 1 0 0 0 0 0 0 0 1 1 0s10 1 1 1 1 0 0 0 0 0 12a20 1 0 0 0 −1 0 0 1 0 2a30 0 1 0 0 0 −1 0 0 1 3s40 0 1 0 0 0 0 1 0 0 80bZ 1 −1 −1 0 0 1 1 0 0 0 −5s10 1 1 1 1 0 0 0 0 0 12 12/1 = 12a20 1 0 0 0 −1 0 0 1 0 2 2/1 = 2a30 0 1 0 0 0 −1 0 0 1 3 –s40 0 1 0 0 0 0 1 0 0 8 –1Z 1 0 −1 0 0 0 1 0 1 0 −3s10 0 1 1 1 1 0 0 −1 0 10 10/1 = 10b 0 1 0 0 0 −1 0 0 1 0 2 –a30 0 1 0 0 0 −1 0 0 1 3 3/1 = 3s40 0 1 0 0 0 0 1 0 0 6 6/1 = 62Z 1 0 0 0 0 0 0 0 1 1 0s10 0 0 1 1 1 1 0 −1 −1 7b 0 1 0 0 0 −1 0 0 1 0 2f 0 0 1 0 0 0 −1 0 0 1 3s40 0 0 0 0 1 1 1 −1 −1 3Phase 2Iter B.V. Z b f r s1s2s3s4RHS Ratio0aZ 1 −10 −2 −5 0 0 0 0 0s10 0 0 1 1 1 1 0 7b 0 1 0 0 0 −1 0 0 2f 0 0 1 0 0 0 −1 0 3s40 0 0 0 0 1 1 1 30bZ 1 0 0 −5 0 −10 −2 0 26s10 0 0 1 1 1 1 0 7 7/1 = 7b 0 1 0 0 0 −1 0 0 2 –f 0 0 1 0 0 0 −1 0 3 –s40 0 0 0 0 1 1 1 3 3/1 = 31Z 1 0 0 −5 0 0 8 10 56s10 0 0 1 1 0 0 −1 4 4/1 = 4b 0 1 0 0 0 0 1 1 5 –f 0 0 1 0 0 0 −1 0 3 –s20 0 0 0 0 1 1 1 3 –2Z 1 0 0 0 5 0 8 5 76r 0 0 0 1 1 0 0 −1 4b 0 1 0 0 0 0 1 1 5f 0 0 1 0 0 0 −1 0 3s20 0 0 0 0 1 1 1 3(b, f, r) = (5, 3, 4) for value of 7612. (45pt)(a) (5pt)max 20f + 10w + 5c + 15wes.t. f + w + 4c + 5w e ≤ 3020f + 20w + 10c + 30we ≤ 168f , w , c , we ≥ 0(b) (10pt)xB= (f, c)B =1 420 10⇒ B−1= −17010 −4−20 1=−1723527−170B−1b =170(372, 432)T= (5.3143, 6.1714)T≥ 0cB= (20, 5)T⇒ cTBB−1A − cT= (0, 10, 0, 10, −1.4286, 1.0714)TTherefore xB= (f, c) is feasbile but not optimal.(c) (15pt)Iter B.V. Z f w c we s1s2RHS Ratio0Z 1 −20 −10 −5 −15 0 0 0s10 1 1 4 5 1 0 30 30/1 = 30s20 20 20 10 30 0 1 168 168/20 = 8.41Z 1 0 10 5 15 0 1 168s10 0 0 3.5 3.5 1 −0.05 21.6f 0 1 1 0.5 1.5 0 0.05 8.4(f, w, c, we) = (8.4, 0, 0, 0) for value of 168(d) (15pt)xB= (s1, f)B =1 10 20⇒ B−1=12020 −10 1=1 −0.050 0.05ˆb = (30, 72)TB−1ˆb = (26.4, 3.6)T≥ 0Therefore xB= (s1, f) remains feasible and optimal.3. (20pt) The provided regression equation is equivalent to the linear programminm,b,tt s.t. ˆxnm + b + t ≥ ˆyn, ˆxnm + b − t ≤
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