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