Hello, Pauline!
This linear programming problem has a feature
. . that makes it quite unusual . . .
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% for the bond fund
and 10% for the stock fund.
Whatever portion of the inheritance he finally decides to commit to the trust fund,
he wants to invest at lesat 30% of that amount in the bond fund.
In addition, he wants a mix with a total return of at least 7.5%.
a. Formulate a linear programming model that can be used to determine the percentage
that should be allocated to the two investment alternatives.
b. Solve the problem using the graphical soluiton procedure.
Let = percentage invested in the bond fund. .
Let = percentage invested in the stock fund. .
So we have: . [1]
We are told that: [2]
The return on the bond fund is: dollars.
The return on the stock fund is; dollars.
. . The total return is: dollars.
The total return is to be at least 7.5% of the total investment:
Hence, we have: . [3]
Graph these statements on a coordinate system.
We are already limited to the first quadrant.
Inequaltiy [2]:
This is the vertical line and the region to the right.
Inequality [3]:
This is the slanted line and the region above it.
So far, we have: Code:
S
 :::::::::::::::::
 ::::::::::::::::
 :::::::::::::::
 ::::::::::::::
 ::::::::::::*
 ::::::::*
 ::::*
 *
 * :
*+ B
 30
But statement [1] is an equation:
There is no "region" . . . the points are on the slanted line. Code:

100 * :
 * :
 * :
 * :
 oA *
 : * *
 : oB
 * *
 * : *
*+*
 30 100
So the "region" is the line segment from to
We find that the maximum return is at point
Therefore, George should invest 30% in bonds and 70% in stocks.