Midterm - Bm&a
Midterm - Bm&a
Project
Consultant
1 2 3 4
A 3 3 5 5
B 3 3 2 4
C 2 1 3 3
D 1 3 1 1
E 3 1 1 2
F 4 5 3 2
Project
Consultant
1 2 3 4
A 0 0 0 450
B 0 0 0 0
C 0 0 235.71429 0
D 0 0 0 0
E 208.33333 0 0 8.5265E-14
F 291.66667 240 164.28571 0
Total hour of each project 500 240 400 450
= = = =
Project Hours 500 240 400 450
Project
1 2 3 4
Total Revenue of each project 100000 36000 62357.143 67500
<= <= <= <=
Contract budget $100,000 $80,000 $120,000 $90,000
rce Project
Project
Hourly wage
5 6 7 8
3 4 3 3 $150
5 5 3 3 $140
2 1 5 3 $160
2 2 5 1 $300
2 3 3 3 $270
3 4 3 3 $150
Project
Consultant
1 2 3 4
A 3 3 5 5
B 3 3 2 4
C 2 1 3 3
D 1 3 1 1
E 3 1 1 2
F 4 5 3 2
Project
Consultant
1 2 3 4
A 0 0 0 211.333333
B 0 0 0 70
C 500 0 2.665E-14 0
D 0 0 0 98.6666667
E 0 240 400 70
F 0 0 0 0
Total hour of each project 500 240 400 450
= = = =
Project Hours 500 240 400 450
Project
1 2 3 4
Total Revenue of each project 80000 64800 108000 90000
<= <= <= <=
Contract budget $100,000 $80,000 $120,000 $90,000
rce Project
Project
Hourly wage
5 6 7 8
3 4 3 3 $150
5 5 3 3 $140
2 1 5 3 $160
2 2 5 1 $300
2 3 3 3 $270
3 4 3 3 $150
Variable Cells
Final Reduced
Cell Name Value Cost
$C$14 A Project 0 -3
$D$14 A 0 -4
$E$14 A 0 0
$F$14 A 450 0
$G$14 A 0 -3
$H$14 A 0 -2
$I$14 A 0 -3.9285714286
$J$14 A 0 -3
$C$15 B Project 0 -2
$D$15 B 0 -3
$E$15 B 0 -2
$F$15 B 0 0
$G$15 B 350 0
$H$15 B 200 0
$I$15 B 0 -2.8571428571
$J$15 B 0 -2
$C$16 C Project 0 -2
$D$16 C 0 -4
$E$16 C 235.71428571 0
$F$16 C 0 0
$G$16 C 0 -2
$H$16 C 0 -3
$I$16 C 264.28571429 0
$J$16 C 0 -1
$C$17 D Project 0 -2
$D$17 D 0 -1
$E$17 D 0 -1
$F$17 D 0 -1
$G$17 D 0 -1
$H$17 D 0 -1
$I$17 D 25.714285714 0
$J$17 D 0 -2
$C$18 E Project 208.33333333 0
$D$18 E 0 -3
$E$18 E 0 -1
$F$18 E 8.526513E-14 0
$G$18 E 0 -1
$H$18 E 95.952380952 0
$I$18 E 0 -1.7857142857
$J$18 E 200 0
$C$19 F Project 291.66666667 0
$D$19 F 240 0
$E$19 F 164.28571429 0
$F$19 F 0 -1
$G$19 F 0 -1
$H$19 F 164.04761905 0
$I$19 F 0 -1.9285714286
$J$19 F 0 -1
Constraints
Final Shadow
Cell Name Value Price
$C$20 Total hour of each project Project 500 3
$D$20 Total hour of each project 240 4
$E$20 Total hour of each project 400 2
$F$20 Total hour of each project 450 2
$G$20 Total hour of each project 350 3
$H$20 Total hour of each project 460 3
$I$20 Total hour of each project 290 2.8571428571
$J$20 Total hour of each project 200 3
$C$26 Total Revenue of each project Project 100000 3.469447E-18
$D$26 Total Revenue of each project = 36000 0
$E$26 Total Revenue of each project = 62357.142857 0
$F$26 Total Revenue of each project = 67500 0
$G$26 Total Revenue of each project = 49000 0
$H$26 Total Revenue of each project = 78514.285714 0
$I$26 Total Revenue of each project = 50000 0.0071428571
$J$26 Total Revenue of each project = 54000 0
$K$14 A Total hour of each consultant used 450 3
$K$15 B Total hour of each consultant used 550 2
$K$16 C Total hour of each consultant used 500 1
$K$17 D Total hour of each consultant used 25.714285714 0
$K$18 E Total hour of each consultant used 504.28571429 0
$K$19 F Total hour of each consultant used 860 1
Objective Allowable Allowable
Coefficient Increase Decrease
3 3 1E+030
3 4 1E+030
5 0 1E+030
5 1E+030 0
3 3 1E+030
4 2 1E+030
3 3.9285714286 1E+030
3 3 1E+030
3 2 1E+030
3 3 1E+030
2 2 1E+030
4 0 1E+030
5 1E+030 1
5 1 0
3 2.8571428571 1E+030
3 2 1E+030
2 2 1E+030
1 4 1E+030
3 1.8 0
3 0 1E+030
2 2 1E+030
1 3 1E+030
5 1 1.8
3 1 1E+030
1 2 1E+030
3 1 1E+030
1 1 1E+030
1 1 1E+030
2 1 1E+030
2 1 1E+030
5 20 1
1 2 1E+030
3 24 4.163336E-16
1 3 1E+030
1 1 1E+030
2 0 0
2 1 1E+030
3 0 0
3 1.7857142857 1E+030
3 1E+030 1
4 4.163336E-16 1.8461538462
5 1E+030 1
3 0 0
2 1 1E+030
3 1 1E+030
4 0 0
3 1.9285714286 1E+030
3 1 1E+030
Project
Consultant
1 2 3 4
A 3 3 5 5
B 3 3 2 4
C 2 1 3 3
D 1 3 1 1
E 3 1 1 2
F 4 5 3 2
Project
Consultant
1 2 3 4
A 0 0 164.28571 285.714286
B 0 0 0 164.285714
C 0 0 235.71429 0
D 0 0 0 0
E 304.28571 0 0 0
F 195.71429 240 0 0
Total hour of each project 500 240 400 450
= = = =
Project Hours 500 240 400 450
Project
1 2 3 4
Total Revenue of each project 90214.286 36000 70571.429 80142.8571
<= <= <= <=
Contract budget $100,000 $80,000 $120,000 $90,000
rce Project
Project
Hourly wage
5 6 7 8
3 4 3 3 $200
5 5 3 3 $140
2 1 5 3 $160
2 2 5 1 $300
2 3 3 3 $200
3 4 3 3 $150
Project
Consultant
1 2 3 4
A 3 3 5 5
B 3 3 2 4
C 2 1 3 3
D 1 3 1 1
E 3 1 1 2
F 4 5 3 2
Project
Consultant
1 2 3 4
A 0 0 0 10
B 0 0 0 70
C 1.99E-13 0 130 370
D 0 240 60 0
E 500 0 210 0
F 0 0 0 0
Total hour of each project 500 240 400 450
= = = =
Project Hours 500 240 400 450
Project
1 2 3 4
Total Revenue of each project 100000 72000 80800 71000
<= <= <= <=
Contract budget $100,000 $80,000 $120,000 $90,000
rce Project
Project
Hourly wage
5 6 7 8
3 4 3 3 $200
5 5 3 3 $140
2 1 5 3 $160
2 2 5 1 $300
2 3 3 3 $200
3 4 3 3 $150
Project
Consultant
1 2 3 4
A 3 3 5 5
B 3 3 3 4
C 2 1 3 3
D 1 3 1 1
E 3 3 3 3
F 4 5 3 2
Project
Consultant
1 2 3 4
A 0 0 0 450
B 0 0 0 0
C 0 0 35.714286 8.5265E-14
D 0 0 0 0
E 140 0 364.28571 0
F 360 240 0 0
Total hour of each project 500 240 400 450
= = = =
Project Hours 500 240 400 450
Project
1 2 3 4
Total Revenue of each project 91800 36000 104071.43 67500
<= <= <= <=
Contract budget $100,000 $80,000 $120,000 $90,000
rce Project
Project
Hourly wage
5 6 7 8
3 4 3 3 $150
5 5 3 3 $140
2 1 5 3 $160
2 2 5 1 $300
3 3 3 3 $270
3 4 3 3 $150
Variable Cells
Final Reduced
Cell Name Value Cost
$C$14 A Project 0 -2
$D$14 A 0 -3
$E$14 A 0 0
$F$14 A 450 0
$G$14 A 0 -2
$H$14 A 0 -1
$I$14 A 0 -4
$J$14 A 0 -2
$C$15 B Project 0 -2
$D$15 B 0 -3
$E$15 B 0 -2
$F$15 B 0 -1
$G$15 B 350 0
$H$15 B 200 0
$I$15 B 0 -4
$J$15 B 0 -2
$C$16 C Project 0 -1
$D$16 C 0 -3
$E$16 C 35.714285714 0
$F$16 C 8.526513E-14 0
$G$16 C 0 -1
$H$16 C 0 -2
$I$16 C 264.28571429 0
$J$16 C 200 0
$C$17 D Project 0 -2
$D$17 D 0 -1
$E$17 D 0 -2
$F$17 D 0 -2
$G$17 D 0 -1
$H$17 D 0 -1
$I$17 D 25.714285714 0
$J$17 D 0 -2
$C$18 E Project 140 0
$D$18 E 0 -1
$E$18 E 364.28571429 0
$F$18 E 0 0
$G$18 E 0 -8.881784E-16
$H$18 E 0 -8.881784E-16
$I$18 E 0 -2
$J$18 E 0 0
$C$19 F Project 360 0
$D$19 F 240 0
$E$19 F 0 -1
$F$19 F 0 -2
$G$19 F 0 -1
$H$19 F 260 0
$I$19 F 0 -3
$J$19 F 0 -1
Constraints
Final Shadow
Cell Name Value Price
$C$20 Total hour of each project Project 500 3
$D$20 Total hour of each project 240 4
$E$20 Total hour of each project 400 3
$F$20 Total hour of each project 450 3
$G$20 Total hour of each project 350 3
$H$20 Total hour of each project 460 3
$I$20 Total hour of each project 290 5
$J$20 Total hour of each project 200 3
$C$26 Total Revenue of each project Project 91800 0
$D$26 Total Revenue of each project = 36000 0
$E$26 Total Revenue of each project = 104071.42857 0
$F$26 Total Revenue of each project = 67500 0
$G$26 Total Revenue of each project = 49000 0
$H$26 Total Revenue of each project = 67000 0
$I$26 Total Revenue of each project = 50000 0
$J$26 Total Revenue of each project = 32000 0
$K$14 A Total hour of each consultant used 450 2
$K$15 B Total hour of each consultant used 550 2
$K$16 C Total hour of each consultant used 500 0
$K$17 D Total hour of each consultant used 25.714285714 0
$K$18 E Total hour of each consultant used 504.28571429 0
$K$19 F Total hour of each consultant used 860 1
Objective Allowable Allowable
Coefficient Increase Decrease
3 2 1E+030
3 3 1E+030
5 0 1E+030
5 1E+030 0
3 2 1E+030
4 1 1E+030
3 4 1E+030
3 2 1E+030
3 2 1E+030
3 3 1E+030
3 2 1E+030
4 1 1E+030
5 1E+030 8.881784E-16
5 8.881784E-16 1
3 4 1E+030
3 2 1E+030
2 1 1E+030
1 3 1E+030
3 0 0
3 0 0
2 1 1E+030
1 2 1E+030
5 0 2.8
3 1E+030 0
1 2 1E+030
3 1 1E+030
1 2 1E+030
1 2 1E+030
2 1 1E+030
2 1 1E+030
5 28 0
1 2 1E+030
3 1 8.881784E-16
3 1 1E+030
3 0 0
3 0 1E+030
3 8.881784E-16 1E+030
3 8.881784E-16 1E+030
3 2 1E+030
3 0 1E+030
4 8.881784E-16 1
5 1E+030 1
3 1 1E+030
2 2 1E+030
3 1 1E+030
4 1 8.881784E-16
3 3 1E+030
3 1 1E+030