
16 Introduction to Linear Optimization and Extensions with MATLAB
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Bond 1 2 3
Price $102 $99 $98
Coupon $5 $3.5 $3.5
Maturity year 1 2 3
The bank wishes to purchase Bonds 1, 2, and 3 in amounts whose total
cash flow will offset the liabilities. Assume that fractional amounts of each
bond are permitted. A linear programming model can be formulated to find
the lowest-cost set of bonds (i.e., portfolio) consisting of Bonds 1, 2, and 3
above that will meet the liabilities. Let the x
i
= amount of bond i purchased.
Then, the problem can be modeled as follows
minimize 102x
1
+ 99x
2
+ 98x
3
subject to 105x
1
+ 3.5x
2
+ 3.5x
3
≥ 12000
103.5x
2
+ 3.5x
3
≥ 18000
103.5x
3
≥ 20000
x
1
,