Hello please help me with these LP problems. Formulate the following problem usi
ID: 3210153 • Letter: H
Question
Hello please help me with these LP problems.
Formulate the following problem 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:
Annual
Bond 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.
Extra Credit (10 Points)
Solve Problem #1 using Excel’s Solver
Explanation / Answer
Total Investment=100,000
Bonds in long term issues = A,C,D
Bonds in short term issues are named= B,E
Tax free investemnts are =A,B,D
Let decision variables are long term issues and short term issues are X and Y respectively.Then
and atleast 50% of investment in shot term issues so,
50000<= 0.5Y(0.08B+0.09
Max Z = 0.5X(0.095A+0.09C+0.09D) + 0.5Y(0.08B+0.09E)
&
The minimum funds should be in tax free investments= 30% = 0.30 x 100,000= $30,000
A+B+D >= 30,000
0.095A+0.09C+0.09D = 0.4[0.5X(0.095A+0.09C+0.09D) + 0.5Y(0.08B+0.09E)]
A & B & C & X & Y >= 0
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