PROBLEMS: Solutions NOT required.

Clearly define decision variables!

$($Media selection$)$ The Milson Co$.$ periodically sponsors public service seminars and programs. Currently, promotional plans

are under way for this year's programs. Advertising alternatives include television, radio, and newspaper. Audience estimates,

costs, and maximum media usage are as shown. $(20$ pts$)$

To ensure a balanced use of advertising media, radio advertisements must not exceed $40\%$ of the total number of

advertisements authorized. In addition, television should account for at least $15\%$ of the total number of advertisements

authorized. Milson has the promotional budget of $$20,000.$

Set up a linear programming model to maximize audience reached.

$($Portfolio selection$)$ Textbook Question $3$: develop the linear programming model. $(20$ pts$)$

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

Automobile loans

Furniture loans

Other secured loans

Signature loans

Risk$-$free securities

Annual Rate of Return $(\%)$

$8$

$10$

$11$

$12$

$9$

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 of the loan$/$investment alternatives to maximize total annual return?