A person wishes to invest R120 000 in three types of bonds:

Question

A person wishes to invest R120 000 in three types of bonds:

 municipal bonds (MF) paying 6% p.a.,
 bank investment certificates (BF) paying 7% p.a. and
 high-risk bonds (HF) paying on average 10% p.a.
For tax purposes, the person wants the amount invested in municipal bonds (MF) to be at
least 2 times the amount invested in the bank certificates (BF).
To lower the level of risk the person will invest no more than R30 000 in high-risk bonds (HF)

Please help me find the equations so that i can solve the problems

Answer 1

I assume you want to maximize

.06m + .07b + .10h

subject to the constraints
m >= 2b
h <= 30000
m+b+h = 120000

plot the lines and pick a vertex.
hint: m+b >= 90000

Answer 2

Thanks Man

this really helped.

Answer 3

To solve this problem, we need to set up some equations based on the given information.

Let's define the variables:
MF = Amount invested in municipal bonds (in Rands)
BF = Amount invested in bank certificates (in Rands)
HF = Amount invested in high-risk bonds (in Rands)

1) The person wishes to invest R120,000 in total, so we have:
MF + BF + HF = 120,000

2) The municipal bonds (MF) should be at least 2 times the amount invested in bank certificates (BF), so we have:
MF >= 2BF

3) The person will invest no more than R30,000 in high-risk bonds (HF), so we have:
HF <= 30,000

Now we have a system of equations. To find the solution, we can use these equations to form a linear programming problem and solve it. Linear programming is a mathematical optimization technique to find the maximum or minimum of a linear function, given certain constraints.

The objective function in this case will be the total return on investment:
Objective function: Return = (0.06 * MF) + (0.07 * BF) + (0.10 * HF)

Constraints:
MF + BF + HF = 120,000
MF >= 2BF
HF <= 30,000

With these equations and constraints, you can set up a linear programming problem and use solver software or linear programming algorithms to find the optimal solution. This will give you the specific amounts to invest in each type of bond that satisfy the given conditions and maximize the return on investment.