Investments for a College Savings Fund. Julia Johnson has been accumulating savings for years to put toward her children's future college educations. She would now like to set up a college$-$savings fund for her two children. The college$-$savings 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 her accumulated savings that she finally decides to commit to the college$-$savings fund, she wants to invest at least $30\%$ of that amount in the bond fund. In addition, she wants to select a mix that will enable her to obtain a total return of at least $7\mathrm{.}5\%.($MLOs $2\mathrm{.}22\mathrm{.}3).$Reminder that you need to include a constraint where the percentages add up to $1.$

a$.$Formulate a linear programming model that can be used to determine the percentage that should be allocated to each of the possible investment alternatives.

b$.$Solve the problem using the graphical solution procedure.