Formulation of a Linear Programming (LP) to maximize the expected return on its investment:

From the given information, let consider “x₁” bet the amount of money invested in bond 1, “x₂” bet the amount of money invested in bond 2, “x₃” bet the amount of money invested in bond 3, “x₄” bet the amount of money invested in bond 4.

The objective is to maximize the expected return on its investments.

z=((percentage of expected annual return on bond 1)(the amount of money invested in bond 1)+(percentage of expected annual return on bond 2)(the amount of money invested in bond 2)+(percentage of expected annual return on bond 3)(the amount of money invested in bond 3)+(percentage of expected annual return on bond 4)(the amount of money invested in bond 4))=0.13x1+0.08x2+0.12x3+0.14x4

Therefore, the objective function is,

Maximize z=0.13x1+0.08x2+0.12x3+0.14x4

Constraint 1:

At least, 8% must be the worst-case return of the bond portfolio.

((percentage of the worst-case annual return on each bond)×(amount of money invested in each bond))1000000≥0.8%0.06x1+0.08x2+0.10x3+0.09x4≥0.08(1000000)0.06x1+0.08x2+0.10x3+0.09x4≥80000

Constraint 2:

At most, the average duration of the bond portfolio must be 6

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Solution Summary: The author explains the objective function of a Linear Programming (LP) to maximize the expected return on its investments.

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