Question

A couple wants to invest up to $20,000. They can purchase corporate bonds yielding a 9.55% return on the amount invested and municipal bonds yielding a 14.25% return on the amount invested. They want to invest at least as much in the corporate bonds as in the municipal bonds. They will also want to invest no more than $14,000 in the municipal bonds. How much should they invest in each type of bond to maximize the return on investment?

what is the municipal bond constraint?

Answer 1

14,000$

Explanation:

To maximize the return on investment, we can set up an optimization problem. Let

�

x be the amount invested in corporate bonds (yielding a 9.55% return), and

�

y be the amount invested in municipal bonds (yielding a 14.25% return). The couple wants to invest at least as much in corporate bonds as in municipal bonds, so we have the constraint

�

≥

�

x≥y.

The total investment should not exceed $20,000, which can be expressed as the constraint

�

+

�

≤

20

,

000

x+y≤20,000.

Additionally, they don't want to invest more than $14,000 in municipal bonds, so we have the constraint

�

≤

14

,

000

y≤14,000.

The objective is to maximize the return, which is given by the following equation:

0.0955

�

+

0.1425

�

0.0955x+0.1425y

Now, we can set up the linear programming problem:

Maximize:

0.0955

�

+

0.1425

�

0.0955x+0.1425y

Subject to:

�

≥

�

x≥y

�

+

�

≤

20

,

000

x+y≤20,000

�

≤

14

,

000

y≤14,000

Solving this linear programming problem will yield the values of

�

x and

�

y that maximize the return on investment while satisfying the given constraints.