Decision variables, objective function, and constraints.

Question

A brokerage firm has just been instructed by one of its clients to invest $350,000 of her money. The analysts at the brokerage firm are considering the following options for investment:

                                              Projected Rate
Investment Option                    of Return (%)
Municipal bonds                               3.5
Company A stocks                         10.0
Company B stocks                          8.2
Company C stocks                          9.0

The client has specified the following guidelines:
- Municipal bonds should constitute at least 30% of the money invested.
- At least 50% of the funds available should be placed in a combination of A, B, and C stocks.
- No more than 40% of the amount invested in municipal bonds should be invested in stock C.

The client’s goal is to maximize total projected return on investments.

Formulate a linear programming model for this investment problem.
(a) Define the decision variables.
(b) Determine the objective function. What does it represent?
(c) Determine all the constraints. Briefly describe what each constraint represents.

Answer 1

Manaal,

 

The decision variables are howinvest to invest in a,b,and c or bonds specifically. The obective function is the total projectedore turn from all options put together, or

.035m+.1a+.082b+.09c

 

Now the constraints. These are the client's specifications. 

municipal bonds are at least thirty percent. Thatmeans,

M>=.3

 

At least fifty percent invested in a,b, and c. That means you can have at most fifty  percent in municipal bonds

M<=.5

 

No more than forty percent invested in municipal bonds should be invested in c. This is a shame because we have to put a fair mount of money in low yielding municipal bonds to be able to invest in nine percent yielding funds in c. So,

C<=.4m

 

They don't ask forAnn answer but already I can see that you would want to put the bare minimum in municipal bonds to put the rest of the funds in A for ten percent yield. However I wouldask if that fifty percent constrains on a,b, and c meant that you had to buy some of each to meet the client's demands.

 

Hope that helps,

Deanna