Porter Investments needs to develop an investment portfolio for Meena Singh from the following list of possible investments.

Investment

Cost

Expected Return

A

$$$$12$ comma $000$

$$$$700$

B

$$$$12$ comma $000$

$$$$1$ comma $000$

C

$$$$3$ comma $500$

$$$$390$

D

$$$$5$ comma $000$

$$$$500$

E

$$$$8$ comma $500$

$$$$750$

F

$$$$8$ comma $000$

$$$$640$

G

$$$$4$ comma $000$

$$$$300$

Singh has a total of $$$$60$ comma $000$ to invest. The following conditions must be$$ met: $(1)$ if investment F is$$ chosen, then investment G must also be part of the$$ portfolio, $(2)$ at least four investments should be$$ chosen, and$(3)$ of investments A and$$ B$,$ exactly one must be included. Formulate and solve this problem using LPLOADING... software to determine which stocks should be included in$$ Singh's portfolio.

Part $2$

For iequals$$A$,$B$,$ C$,$ D$,$ E$,$ F$,$ G$,$ we define the decision variablesLOADING....

Let iequalsleft brace Start $2$ By $1$ Matrix $1$st Row $1$st Column $1$ if investment i is chosen $2$nd Row $1$st Column $0$ otherwise EndMatrix

Part $3$

Write the objective functionLOADING... and the constraintLOADING... in equations.

Maximize expected returnequals

$$

$700$ Upper A plus $1$ comma $000$ Upper B plus $390$ Upper C minus $500$ Upper D minus $750$ Upper E minus $640$ Upper F minus $300$ Upper G

$700$ Upper A plus $1$ comma $000$ Upper B plus $390$ Upper C plus $500$ Upper D plus $750$ Upper E plus $640$ Upper F plus $300$ Upper G

$12$ comma $000$ Upper A plus $12$ comma $000$ Upper B plus $3$ comma $500$ Upper C plus $5$ comma $000$ Upper D plus $8$ comma $500$ Upper E plus $8$ comma $000$ Upper F plus $4$ comma $000$ Upper G

$11$ comma $300$ Upper A plus $11$ comma $000$ Upper B plus $3$ comma $110$ Upper C plus $4$ comma $500$ Upper D plus $7$ comma $750$ Upper E plus $7$ comma $360$ Upper F plus $3$ comma $700$ Upper G

Expected return is equal to the sum of the products of the returns and the decision variables.

Part $4$

Subject$$ to:

Part $5$Part $6$Part $7$Part $8$

Total investment$$ constraint:

$$

$700$ Upper A plus $1$ comma $000$ Upper B plus $390$ Upper C plus $500$ Upper D plus $750$ Upper E plus $640$ Upper F plus $300$ Upper G #$38$ le

$12$ comma $000$ Upper A plus $12$ comma $000$ Upper B plus $3$ comma $500$ Upper C plus $5$ comma $000$ Upper D plus $8$ comma $500$ Upper E plus $8$ comma $000$ Upper F plus $4$ comma $000$ Upper G #$38$ ge

$700$ Upper A plus $1$ comma $000$ Upper B plus $390$ Upper C plus $500$ Upper D plus $750$ Upper E plus $640$ Upper F plus $300$ Upper G #$38$ ge

$12$ comma $000$ Upper A plus $12$ comma $000$ Upper B plus $3$ comma $500$ Upper C plus $5$ comma $000$ Upper D plus $8$ comma $500$ Upper E plus $8$ comma $000$ Upper F plus $4$ comma $000$ Upper G #$38$ le

Constraint for condition$1$: If investment F is$$ chosen, then investment G must also be part of the$$ portfolio:

$$

Upper F #$38$ ge

Upper F #$38$ gt

Upper F #$38$ lt

Upper F plus Upper G equals $0$

Upper F #$38$ le

Upper F equals Upper G

Constraint for condition$2$: At least four investments should be$$ chosen:

$$

Upper A plus Upper B plus Upper E plus Upper F plus Upper G #$38$ ge

Upper A plus Upper B plus Upper C plus Upper D plus Upper E plus Upper F plus Upper G #$38$ ge

Upper A plus Upper B plus Upper C plus Upper D plus Upper E #$38$ ge

Upper A plus Upper B plus Upper C plus Upper D plus Upper E plus Upper F plus Upper G #$38$ Le

Constraint for condition$3$: Of investments A and$$ B$,$ exactly one must be$$ included:

$$

Upper A equals Upper B

Upper A plus Upper B equals $0$

Upper A #$38$ ge

Upper A #$38$ Le

Upper A plus Upper B equals $1$

Upper A plus Upper B equals $2$

Constraint for decision$$ variables:

$$A$,$ B$,$ C$,$ D$,$ E$,$ F$,$ G

$$

equals $0$

#$38$ ge

equals $0$ or $1$

equals $1$

#$38$ le

Part $9$

The maximum expected return is $$$

$$

enter your response here.

Part $10$

Select the$$ investment$($s$)$ that should be included in$$ Singh's portfolio. $($Select all that$$ apply.$)$

E

B

D

F

G

C

A

Maximize expected returnExpected return is equal to the sum of the products of the returns and the decision variables.Expected return is equal to the sum of the products of the returns and the decision variables.Subject to:listbox $4,$listbox $5,$listbox $6,$The maximum expected return is $$.)$