A trust officer for the Million Bank wants to invest in the following bonds.
Bond Yield Maturity Risk Tax- Free
A 8% Long High Yes
B 9 Short Low No
C 9 Long High No
D 10 Short Low No
E 9 Short High Yes

She will use a linear program to find the dollar investment in each bond that will maximize total interest income.
a.) Define the variables that apply and then express her linear programming objective in terms of these.

b.) Express each of the following linear programming constraints using the variables defined in (a).

1. Exactly $100,000 will be invested altogether.
2. At least $50,000 must be placed in short maturity bonds.
3. No more than $30,000 may be invested in high-risk issues.
4. At least $25,000 must be placed in tax-free issues.
5. Total funds invested in low-risk bonds must be less than or equal to total funds placed in long-maturity issues.
6. The interest income derived from tax-free bonds must be at least one-fourth of the total income.