George johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. the trust fund has two investment options:

(1) a bond fund and
(2) a stock fund.

the projected returns over the life of the investments are 9% for the bond fund and 20% for the stock fund. whatever portion of the inheritance he finally decides to commit to the trust fund, he wants to invest at least 60% of that amount in the bond fund. in addition, he wants to select a mix that will enable him to obtain a total return of at least 8.5%.

a) formulate a linear programming model that can be used to determaine the percentage that should be allocated to each of the possible i nvestment alternatives

b) solve the problem using the graphical solution procedure.

Max0.09B+0.2s  

 B>=0.6Bond fund minimum

 0.06B+0.2S>=0.085Minimum Return

 B+S=1All funds invested

 B,S>=0

Step-by-step explanation:

(a) In linear programming,  the  mathematical model and the linear objective function set of linear constraints the variables are not negative.

B=% funds invested in the bond fund

S=% of funds invested in the stock fund

Max0.09B+0.2s  

 B>=0.6Bond fund minimum

 0.06B+0.2S>=0.085Minimum Return

 B+S=1All funds invested

 B,S>=0

Solve the above by using the graphical solution procedure?

steps to solve the graphs

1)draw the graphs, making sure the constraints are consider

2)consider all the constraints

3)draw the objective function line to the decision variables to

4) place the parallel lines of objective function towards larger objective function

5)  consider as optimal function  the feasible solution on the objective function line with the largest value ia

6e14 is the answer.