|\^/| Maple 18 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > read `your_task190`; Your boss says: hire UG markers, GTA's, profs, so that (0) you pay UG's $12/hour, GTA's $11/hour, profs $3/hour; (1) you have 3 hours of teaching per week, done by the profs; (2) you have 6 hours of writing homeworks and solutions, done by GTA's or profs; (3) you have 12 hours of homework marked by UG markers or GTA's; (4) you have at least twice as many UG hours per week than prof hours; and (5) you spend at most $190 per week. Let x1=marker hours, x2=TA marking hours, x3=TA writing hours. Let x4=prof writing hours, x5=prof teaching. eqns := {w1 = x5 - 3 const + x0, w2 = x3 + x4 - 6 const + x0, w3 = x1 + x2 - 12 const + x0, w4 = x1 - 2 x4 - 2 x5 + x0, w5 = 190 const - 12 x1 - 11 x2 - 11 x3 - 3 x4 - 3 x5 + x0, zz = -x0} basic := [zz, w1, w2, w3, w4, w5] nonbasic := [x0, x1, x2, x3, x4, x5] Dictionary: basic = [zz, w1, w2, w3, w4, w5], non-basic = [x0, x1, x2, x3, x4, x5] zz = -x0 w1 = -3 const + x0 + x5 w2 = -6 const + x0 + x3 + x4 w3 = -12 const + x0 + x1 + x2 w4 = x0 + x1 - 2 x4 - 2 x5 w5 = 190 const + x0 - 12 x1 - 11 x2 - 11 x3 - 3 x4 - 3 x5 Try mypivot(x0,w3). Ready? Basic variables: [zz, w1, w2, x0, w4, w5], [w3, x1, x2, x3, x4, x5], nonbasic variables: Dictionary: basic = [zz, w1, w2, x0, w4, w5], non-basic = [w3, x1, x2, x3, x4, x5] zz = -12 const - w3 + x1 + x2 w1 = 9 const + w3 - x1 - x2 + x5 w2 = 6 const + w3 - x1 - x2 + x3 + x4 x0 = 12 const + w3 - x1 - x2 w4 = 12 const + w3 - x2 - 2 x4 - 2 x5 w5 = 202 const + w3 - 13 x1 - 12 x2 - 11 x3 - 3 x4 - 3 x5 Try mypivot(x1,w2). Ready? Basic variables: [zz, w1, x1, x0, w4, w5], [w3, w2, x2, x3, x4, x5], nonbasic variables: Dictionary: basic = [zz, w1, x1, x0, w4, w5], non-basic = [w3, w2, x2, x3, x4, x5] zz = -6 const - w2 + x3 + x4 w1 = 3 const + w2 - x3 - x4 + x5 x1 = 6 const + w3 - w2 - x2 + x3 + x4 x0 = 6 const + w2 - x3 - x4 w4 = 12 const + w3 - x2 - 2 x4 - 2 x5 w5 = 124 const - 12 w3 + 13 w2 + x2 - 24 x3 - 16 x4 - 3 x5 Try mypivot(x3,w1). Ready? Basic variables: [zz, x3, x1, x0, w4, w5], [w3, w2, x2, w1, x4, x5], nonbasic variables: Dictionary: basic = [zz, x3, x1, x0, w4, w5], non-basic = [w3, w2, x2, w1, x4, x5] zz = -3 const - w1 + x5 x3 = 3 const + w2 - w1 - x4 + x5 x1 = 9 const + w3 - x2 - w1 + x5 x0 = 3 const + w1 - x5 w4 = 12 const + w3 - x2 - 2 x4 - 2 x5 w5 = 52 const - 12 w3 - 11 w2 + x2 + 24 w1 + 8 x4 - 27 x5 Try mypivot(x5,w5). Ready? Basic variables: [zz, x3, x1, x0, w4, x5], [w3, w2, x2, w1, x4, w5], nonbasic variables: Dictionary: basic = [zz, x3, x1, x0, w4, x5], non-basic = [w3, w2, x2, w1, x4, w5] zz = 29 const 4 w3 11 w2 x2 w1 8 x4 w5 - -------- - ---- - ----- + ---- - ---- + ---- - ---- 27 9 27 27 9 27 27 x3 = 133 const 4 w3 16 w2 x2 w1 19 x4 w5 --------- - ---- + ----- + ---- - ---- - ----- - ---- 27 9 27 27 9 27 27 x1 = 295 const 5 w3 11 w2 26 x2 w1 8 x4 w5 --------- + ---- - ----- - ----- - ---- + ---- - ---- 27 9 27 27 9 27 27 x0 = 29 const 4 w3 11 w2 x2 w1 8 x4 w5 -------- + ---- + ----- - ---- + ---- - ---- + ---- 27 9 27 27 9 27 27 w4 = 220 const 17 w3 22 w2 29 x2 16 w1 70 x4 2 w5 --------- + ----- + ----- - ----- - ----- - ----- + ---- 27 9 27 27 9 27 27 x5 = 52 const 4 w3 11 w2 x2 8 w1 8 x4 w5 -------- - ---- - ----- + ---- + ---- + ---- - ---- 27 9 27 27 9 27 27 Try mypivot(x2,w4). Ready? Basic variables: [zz, x3, x1, x0, x2, x5], [w3, w2, w4, w1, x4, w5], nonbasic variables: Dictionary: basic = [zz, x3, x1, x0, x2, x5], non-basic = [w3, w2, w4, w1, x4, w5] zz = 23 const 11 w3 11 w2 w4 5 w1 6 x4 w5 - -------- - ----- - ----- - ---- - ---- + ---- - ---- 29 29 29 29 29 29 29 x3 = 151 const 11 w3 18 w2 w4 5 w1 23 x4 w5 --------- - ----- + ----- - ---- - ---- - ----- - ---- 29 29 29 29 29 29 29 x1 = 105 const 33 w3 33 w2 26 w4 43 w1 76 x4 3 w5 --------- - ----- - ----- + ----- + ----- + ----- - ---- 29 29 29 29 29 29 29 x0 = 23 const 11 w3 11 w2 w4 5 w1 6 x4 w5 -------- + ----- + ----- + ---- + ---- - ---- + ---- 29 29 29 29 29 29 29 x2 = 220 const 51 w3 22 w2 27 w4 48 w1 70 x4 2 w5 --------- + ----- + ----- - ----- - ----- - ----- + ---- 29 29 29 29 29 29 29 x5 = 64 const 11 w3 11 w2 w4 24 w1 6 x4 w5 -------- - ----- - ----- - ---- + ----- + ---- - ---- 29 29 29 29 29 29 29 Try mypivot(x4,x2). Ready? Basic variables: [zz, x3, x1, x0, x4, x5], [w3, w2, w4, w1, x2, w5], nonbasic variables: Dictionary: basic = [zz, x3, x1, x0, x4, x5], non-basic = [w3, w2, w4, w1, x2, w5] zz = const 8 w3 11 w2 4 w4 11 w1 3 x2 w5 - ----- - ---- - ----- - ---- - ----- - ---- - ---- 7 35 35 35 35 35 35 x3 = 19 const 67 w3 13 w2 19 w4 13 w1 23 x2 2 w5 -------- - ----- + ----- + ----- + ----- + ----- - ---- 7 70 35 70 35 70 35 x1 = 83 const 27 w3 11 w2 4 w4 11 w1 38 x2 w5 -------- + ----- - ----- - ---- - ----- - ----- - ---- 7 35 35 35 35 35 35 x0 = const 8 w3 11 w2 4 w4 11 w1 3 x2 w5 ----- + ---- + ----- + ---- + ----- + ---- + ---- 7 35 35 35 35 35 35 x4 = 22 const 51 w3 11 w2 27 w4 24 w1 29 x2 w5 -------- + ----- + ----- - ----- - ----- - ----- + ---- 7 70 35 70 35 70 35 x5 = 20 const 8 w3 11 w2 4 w4 24 w1 3 x2 w5 -------- - ---- - ----- - ---- + ----- - ---- - ---- 7 35 35 35 35 35 35 Done. 11 * w1 + 11 * w2 + 8 * w3 + 4 * w4 + w5 is: -5 const + 35 x0 - 3 x2