The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk$-$free securities to stabilize income. The various revenue$-$producing investments together with annual rates of return are as follows:

Type of Loan$/$Investment

Annual Rate of Return $(\%)$

Automobile loans

$8$

Furniture loans

$10$

Other secured loans

$11$

Signature loans

$12$

Risk$-$free securities

$9$

The credit union will have $$2$ million available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments:

Risk$-$free securities may not exceed $30\%$ of the total funds available for investment.

Signature loans may not exceed $10\%$ of the funds invested in all loans $($automobile$,$ furniture, other secured, and signature loans$).$

Furniture loans plus other secured loans may not exceed the automobile loans.

Other secured loans plus signature loans may not exceed the funds invested in risk$-$free securities$.$

We want to maximize total annual return.

Determine the number of decision variables.

Group of answer choices

$5$

$4$

$6$

$3$

Flag question: Question $2$

Question $21$ pts

How much should be invested in risk$-$free securties to maximize total annual return?

Group of answer choices

$600000$

$500000$

$630000$

$170000$

Flag question: Question $3$

Question $31$ pts

How much should be allocated to automobile loans to maximize total annual return?

Group of answer choices

$630000$

$170000$

$140000$

$460000$

Flag question: Question $4$

Question $41$ pts

What is the projected total annual return?

Group of answer choices

$188800$

$200000$

$198000$

$150000$

Flag question: Question $5$

Question $51$ pts

How many constraint$($s$)$ are binding?

Group of answer choices

$5$

$1$

$4$

$3$

Flag question: Question $6$

Question $61$ pts

What is the projected total annual return if the amount the credit union have to invest increase from $$2,000,000$ to $$2,000,100?$

Group of answer choices

$188809\mathrm{.}20$

$188800\mathrm{.}09$

$198900\mathrm{.}09$

$200100\mathrm{.}09$

Flag question: Question $7$

Question $71$ pts

What are the right$-$hand side value$($s$)$ of all the less than or equal to $($

$<=$

$)$ constraints?

Group of answer choices

$0$

$1$

$2$

$3$

Flag question: Question $8$

Question $81$ pts

What is the allowabe increase for right$-$hand size of the following constraint for which the shadow price remains valid?

Constraint: Signature loans may not exceed $10\%$ of the funds invested in all loans $($automobile$,$ furniture, other secured, and signature loans$).$

Group of answer choices

$460000$

$140000$

$500000$

$250000$