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# Multiple choice questions

Find the complete optimal solution to this linear programming problem.

Min 5X + 6Y
s.t. 3X + Y >= 15
X + 2Y >= 12
3X + 2Y >= 24
X,Y >=0

x=3,y=3,z=48,s1=6,s2=0,s3=0
x=6,y=3,z=48,s1=6,s2=0,s3=0
x=3,y=6,z=48,s1=3,s2=0,s3=0
x=6,y=3,z=52,s1=6,s2=0,s3=0

I think the correct answer is x=3,y=6,z=48,s1=3,s2=0,s3=0

The optimal solution of the linear programming problem is at the intersection of constraints 1 and 2.

Max 2x1 + x2
s.t. 4x1 + 1x2<=400
4x1 + 3x2 <= 600
1x1 + 2x2 <= 300
x1,x2 >=0

Compute the dual prices for the three constraints
.45, .25, 0
.25, .25, 0
0, .25, .45
.45, .25, .25

I think the correct answer is .45, .25, .25

In the linear programming formulation of a transportation network
there is one constraint for each node

there is one variable for each arc

the sum of variables corresponding to arcs out of an origin node is constrained by the supply at that node

All of the above are correct

I think the correct answer is All of the above