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 least 30 % 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 7.5 %. 

1. If you are solving large scale Linear Programming (LP) problems with quite a few constraints to manage your scarce resources, and if you are requested to use the resource(s) to the full extent, would you formulate them as equalities; why? why not? 

2. When you do have some constraints as equalities; what happens to your possible solutions? 

3. What are your decision variables? (please don't forget the unit of measurements for them) 

4. Why have you allocated 30% of the portfolio to the bonds though restriction was 30% or more? 

5. What will happen to your total return if you had to allocate more than 30% (say 31%) of the portfolio to the bonds?