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Investor Group specialized in recommending long-term financial portfolios for wealthy clients. One such client wishes to invest $4,000,000 in the following bonds: Company Return Acme

Investor Group specialized in recommending long-term financial portfolios for wealthy clients. One such client wishes to invest $4,000,000 in the following bonds:

Company Return
Acme chemical 3.5%
DynaStar 10.50%
Eagle Vision 12.75%
Micro Modeling 6.75%
OptiPro 15.25%
Sabre Systems 17.80%

The client has made the following specifications:

At least 3% should be invested in each company.

At least 35% is invested in DynaStar, Micro Modeling, and Sabre Systems.

Investor Group formulates this investment problem as a Linear Programming model that maximizes total returns, given the company's specifications. Nonnegative decision variables X1, X2, X3, X4, X5, X6 are defined that respectively represent the amount of money (in dollars) that is invested in Acme Chemical, DynaStar, Eagle Vision, MicroModeling, OptiPro, and Sabre Systems.

Which of the following models represents the LP formulation?

Question 12 options:

a)

Maximize Return= 0.035 X1+ 0.105 X2+ 0.1275 X3+ 0.0675 X4+ 0.1525 X5+ 0.1780 X6

Subject to

X1 + X2 + X3 + X4 + X5 + X6 4,000,000

X1 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X2 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X3 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X4 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X5 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X6 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X2 + X4 + X6 0.35(X1 + X2 + X3 + X4 + X5 + X6)

All variables are nonnegative

b)

Maximize Return= 0.035 X1+ 0.105 X2+ 0.1275 X3+ 0.0675 X4+ 0.1525 X5+ 0.1780 X6

Subject to

X1 + X2 + X3 + X4 + X5 + X6 4,000,000

X1 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X2 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X3 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X4 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X5 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X6 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X2 + X4 + X6 0.35(X1 + X2 + X3 + X4 + X5 + X6)

All variables are nonnegative

c)

Maximize Return= 0.035 X1+ 0.105 X2+ 0.1275 X3+ 0.0675 X4+ 0.1525 X5+ 0.1780 X6

Subject to

X1 + X2 + X3 + X4 + X5 + X6 4,000,000

X1 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X2 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X3 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X4 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X5 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X6 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X2 + X4 + X6 0.35(X1 + X2 + X3 + X4 + X5 + X6)

All variables are nonnegative

d)

Maximize Return= 0.035 X1+ 0.105 X2+ 0.1275 X3+ 0.0675 X4+ 0.1525 X5+ 0.1780 X6

Subject to

X1 + X2 + X3 + X4 + X5 + X6 4,000,000

X1 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X2 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X3 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X4 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X5 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X6 0.03 (X1 + X2 + X3 + X4 + X5 + X6)

X2 + X4 + X6 0.35(X1 + X2 + X3 + X4 + X5 + X6)

All variables are nonnegative

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