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 6 percent for the bond fund and 10 percent for the stock fund.Whatever portion of the inheritance he finally decides to commit to the trust fund, he wants to invest atleast 30 percent 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 atleast 7.5 percent.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 alternativesB) Solve the problem using the graphical solution procedure.

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Asked Apr 18, 2019
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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 6 percent for the bond fund and 10 percent for the stock fund.Whatever portion of the inheritance he finally decides to commit to the trust fund, he wants to invest atleast 30 percent 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 atleast 7.5 percent.

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.

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Expert Answer

Step 1

(a) In the linear program the general mathematical model and the linear objective function set of linear constraints the variables are nonnegative.

B=Percentage of funds invested in the bond fund

S=percentage of funds invested in the stock fund

Max0.06B+0.1s 
 B>=0.3Bond fund minimum
 0.06B+0.1S>=0.075Minimum Return
 B+S=1All funds invested
 B,S>=0 
Step 2

(b)Solve the problem using the graphical solution procedure?

We have 5basic steps to solve the graphical solution

1)first draw the graph for each the constraint it will shows the solution to satisfy the constraints.

2)identify the solution to satisfy all the constraints

3)And also draw the objective function line to the decision variables to specified value of the function.

4)After that miove the parallel lines of objective function towards larger objecti ve function

5)Then any feasible solution on the objective function line with the largest value ia to be consider as optimal function.

Step 3

Then the basic considerations are 

B=0.3

...

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