ch19 - 19-1 19-2 19.3 By using Excel-Solver, this...

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Unformatted text preview: 19-1 19-2 19.3 By using Excel-Solver, this optimization problem is quickly solved. The selected starting point is (1,1): X1X2Initial values 1 1 Final values 0.776344 0.669679 max Y= 0.55419 Constraints 0 ≤X1 ≤2 0 ≤X2 ≤2 Table S19.3.Excel solution Hence the optimum point is ( X1*, X2* ) =(0.776, 0.700) and the maximum value of Yis Ymax = 0.554 19.4 Let Nbe the number of batches/year. Then NP≥300,000 Since the objective is to minimize the cost of annual production, only the required amount should be produced annually and no more. That is, NP= 300,000 (1) a)Minimize the total annual cost, min TC= 400,000 $batch+ 2 P0.4hrbatch50$hrNbatchyr+ 800 P0.7yr$Substituting for Nfrom (1) gives min TC= 400,000 + 3x107P–0.6+ 800 P0.719-3 b)There are three constraints on Pi)P≥0 ii)Nis integer. That is, (300,000/P) = 0, 1, 2,… iii)Total production time is 320 x 24 hr/yr (2 P0.4+ 14)hrbatch×Nbatchyr≤7680 Substituting for Nfrom (1) and simplifying 6×105P-0.6+ 4.2×106P-1 ≤7680 c) 71.60.3()3 10 ( 0.6)800(0.7)d TCPPdP--==×-+1/1.373 10 ( 0.6)lb2931800(0.7)batchoptP×-==-272.61.32()3 10 ( 0.6)( 1.6)800(0.7)( 0.3)dTCPPdP--=×--+-222()2.26 10optP PdTCdP-==×〉hence minimum Nopt= 300,000/Popt= 102.35 not an integer. Hence check for Nopt= 102 and Nopt= 103 For Nopt = 102, Popt= 2941.2, and TC= 863207 For Nopt= 103, Popt= 2912.6, and TC= 863209 Hence optimum is 102 batches of 2941.2 lb/batch. Time constraint is 50.6616 104.2 106405.87680PP--×+×=≤, satisfied 19-4 19.5 Let x1be the daily feed rate of Crude No.1 in bbl/day x2be the daily feed rate of Crude No.2 in bbl/day Objective is to maximize profit max P= 2.00 x1+ 1.40 x2Subject to constraints gasoline : 0.70 x1+ 0.31 x2 ≤6000 kerosene: 0.06 x1+ 0.09 x2 ≤2400 fuel oil: 0.24 x1+ 0.60 x2≤12,000 By using Excel-Solver, x1x2Initial values 1 1 Final values 0 19354.84 max P= 27096.77 Constraints 0.70 x1+ 0.31 x26000 0.06 x1+ 0.09 x21741.935 0.24 x1+ 0.60 x211612.9 Table S19.5. Excel solution Hence the optimum point is (0, 19354.8) Crude No.1 = 0 bbl/day Crude No.2 = 19354.8 bbl/day 19-5...
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This homework help was uploaded on 04/10/2008 for the course CHE 242 taught by Professor Cummings during the Spring '08 term at Vanderbilt.

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ch19 - 19-1 19-2 19.3 By using Excel-Solver, this...

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