Question: Consider the following linear programming problem Max 8X + 5Y s.t. 15X + 5Y 120 10X + 6Y 90 X + Y 12 X, Y
Consider the following linear programming problem
| Max | 8X + 5Y |
| s.t. | 15X + 5Y 120 |
|
| 10X + 6Y 90 |
|
| X + Y 12 |
|
| X, Y 0 |
| a. | List all the extreme points of the feasible region. |
| b. | Find the optimal solution and the objective function value. |
| c. | List the values of all the slack variables. |
A
a. (0,0), (4,0), (6.75,3.75), (4.5,7.5), (0,6); b. x=4.5, y=7.5, OFV=73.5; c. s1=15 , s2=0 , s3=0.
B
a. (0,0), (8,0), (6.75,3.75), (4.5,7.5), (0,12); b. x=6.75, y=3.75, OFV=72.75; c. s1=0 , s2=0 , s3=1.5.
C
a. (0,0), (9,0), (6.75,3.75), (4.5,7.5), (0,15); b. x=0, y=15, OFV=75; c. s1=45 , s2=0 , s3=3.
D
a. (0,0), (8,0), (8,6), (4.5,7.5), (0,12); b. x=8, y=6, OFV=94; c. s1=0 , s2=0 , s3=2.
E
a. (0,0), (8,0), (6,6), (4.5,7.5), (0,24); b. x=0, y=24, OFV=120; c. s1=0 , s2=54 , s3=12
F
a. (0,0), (8,0), (6.75,3.75), (6,6), (0,12); b. x=6, y=6, OFV=78; c. s1=0 , s2=6 , s3=0
G
a. (0,0), (8,0), (6.75,3.75), (6,8), (0,12); b. x=6, y=8, OFV=88; c. s1=10 , s2=0 , s3=0.
H
a. (0,0), (8,0), (6.75,3.75), (4.5,7.5), (0,12); b. x=4.5, y=7.5, OFV=73.5; c. s1=15 , s2=0 , s3=0.
I
a. (0,0), (12,0), (6.75,3.75), (4.5,7.5), (0,12); b. x=12, y=0, OFV=96; c. s1=60 , s2=30 , s3=0.
J
a. (0,0), (8,0), (6,6), (4.5,7.5), (0,12); b. x=6, y=6, OFV=78; c. s1=0 , s2=6 , s3=0.
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