i have question on quantitative methods for business 12th edition chapter 9 p3. which is Liner Programming problems. the question goes like this

the employee credit union at state university is planning the allocation of fund for the coming year. the credit union makes four types of loans to its member. 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

i have question on quantitative methods for business 12th edition chapter 9 p3. the question goes like this

the employee credit union at state university is planning the allocation of fund for the coming year. the credit union makes four types of loans to its member. 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.

How should the $2 million be allocated to each loan/investment alternative to maximize total annual return?

What is the projected total annual return?

please only do this part below

In 12-11 , suppose the following 2 changes have occurred:

• The total amount available for investment is $1.5 million.
• An additional constraint is: auto loans plus furniture loans must not exceed 40% of the funds invested in all loans (automobile, furniture, other secured, and signature loans).

Write down the corresponding two constraints. Use variable names:

A = $ automobile loans

F = $ furniture loans

O = $ other secured loans

S = $ signature loans

R = $ "risk free" securities