https://www.onlinemathe.de/forum/Vollauslastung-soll-ermittelt-werden[br] [br] [br][table] [tr][br] [td]Drei Artikel A1, A2, A3 durchlaufen[br]nacheinander die Produktionstellen [br]Ma1, Ma2, Ma3:[br][br]Produktionszeiten t[sub]max[/sub] [min/stück][/td][td][/td][br] [td]Three items A1, A2, A3 pass through [br]the production stations Ma1, Ma2, Ma3 [br]in sequence:[br][br]Production times t[sub]max [/sub][min/item][/td][br][/tr][br][tr][br][td][br][/td][td][br][math]\large\begin{tabular}{ccccccc} & Ma1 & Ma2 & Ma3 \\ A1 & 4 & 6 & 8 \\ A2 & 10 & 8 & 2 \\ A3 & 9 & 5 & 10\\t_{max} & 540 & 600 & 570\\ \end{tabular}[/math][/td][br][td][br][/td][/tr][br][tr][td]Bestimmen Sie das optimale Produktionsprogramm für [br]Vollauslastung ohne Berücksichtigung der Produktionsabfolge.[br][/td][td][/td][br] [td]Determine the optimal production program for full capacity utilization without taking the production sequence into account.[br][br][/td][/tr][/table][br][br]maximize_lp([br]24*x3+20*x2+18*x1,[[br]9*x3+10*x2+4*x1 <= 540, [br]5*x3+8*x2+6*x1 <= 600, [br]10*x3+2*x2+8*x1 <= 570[br]]), numer;[br]do Branch & Bound as described in the app - add step wise constraints x3=2, x2=27[br][math]\textcolor{blue}{\large\mathcal{SageMath-Link}\nearrow[/math] [br]https://sagecell.sagemath.org/?q=fnbtqj[br][br][math]Tablo \, := \, \left\{ 4 \; x1 + 10 \; x2 + 9 \; x3 = 540, 6 \; x1 + 8 \; x2 + 5 \; x3 = 600, 8 \; x1 + 2 \; x2 + 10 \; x3 = 570, -18 \; x1 - 20 \; x2 - 24 \; x3 = 0 \right\} [/math][br][br][br][b][color=#0b5394]Branch & Bound [/color][/b][color=#0b5394][b]addtions[/b][br][i]IL[sub]20[/sub], IL[sub]30[/sub] [/i][br]results of Simplex-EndTab of Branch[br][i]downIL[sub]20[/sub], downIL[sub]30[/sub] [/i][br]results alternately round down to integer[br][i]downZ[sub]20[/sub], downZ[sub]30[/sub][/i][br]test objective (Z) for best optimization result[br][i]Join({{0,0,1,0,0,0,2}},Start)[br]Join({{0,1,0,0,0,0,27}},A_{21})[br]add x[sub]i[/sub] to Start-Tab of Branch and execute [/i]gauss-step to implement x[sub]i[/sub] value in Tab[br]no round up test to keep things simpler [br][/color][br][br][math]\textcolor{blue}{\large\mathcal{SageMath-Link}\nearrow[/math] [br] [url=https://sagecell.sagemath.org/?q=ztpddp]sagecell.sagemath.org/?q=ztpddp[/url]