Formulate the following problems using the following steps.

a. Define the decision variables.

b. Specify the objective function.

c. Specify the constraints and simplify them so that the left hand side of each constraint only contains terms involving the decision variables.

A trust officer at the Blackburg National Bank needs to determine how to invest $100,000 in the following collection of bonds to maximize the annual return. The information is given in the following table:

Bond Annual Return(%) Maturity Risk Tax Free

A 9.5 Long High Yes

B 8.0 Short Low Yes

C 9.0 Long Low No

D 9.0 Long High Yes

E 9.0 Short High No

The officer wants to invest at least 50% of the money in short-term issues and no more than 50% in high risk issues. At least 30% of the funds should go in tax-free investments and at least 40% of the total return should be tax free. Formulate as an LP.