Investing in Bonds A woman wishes to invest $12,000 in three types of bonds: municipal bonds paying 7% interest per year, bank certificates paying 8%, and high-risk bonds paying 12%. For tax reasons she wants the amount invested in municipal bonds to be at least three times the amount invested in bunk certificates. To keep her level of risk manage-able, she will invest no more than $2000 in high-risk bonds. How much should she invest in each type of bond to maximize her annual interest yield? [Hint: Let x = amount in municipal bonds and y = amount in bunk certificates. Then the amount in high-risk bonds will be 12,000 − x − y.]
To find: The amount money a women invest in the municipal bond, bank certificate bond and high-risk bond for the maximum interest.
Answer to Problem 13P
Women invest
Explanation of Solution
Given:
The total amount of money is
The municipal bond pays
The amount of money a women invested in municipal bond is three times the invested in bank certificates.
Women invest no more than
Calculation:
Suppose the amount invested in the municipal bond is x and the amount invested in the bank certificate bond is y for the maximum interest.
Then the amount invested in the high risk bond is
Use the given information to make the inequalities and the objective function for the feasible region.
The required information is shown in the table below.
municipal bond | Bank certificate bond | high-risk bond | |
Amount of money | x | y |
|
The objective function is,
The constraint to get the feasible region has shown below.
Now, take the equalities of the above inequalities,
And,
And,
And,
Substitute
Substitute 2500 for y in equation (3),
The intersection point is
Substitute
Substitute 3000 for y in equation (3),
Now, draw the graph of the above equations,
Figure (1)
The vertices which lies in the feasible region is shown below.
Substitute the 7500 for x and 2500 for y in the objective function
Substitute the 10000 for x and 0 for y in the objective function
Substitute the 12000 for x and 0 for y in the objective function
Substitute the 9000 for x and 3000 for y in the objective function
So, all the satisfies these vertices are shown in the table below.
Vertices |
|
| 965(Maximum) |
| 940 |
| 840 |
| 960 |
The maximum interest rate is 965 at the investment
Thus, a women invest
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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