Question

An investment firm offers three types of investments to its clients. To help a client make a better-informed decision, each investment is assigned a risk factor. The risk factor and expected return of each investment are the following:

Investment A: 12% return per year, risk factor=0.50 Investment
B: 15% return per year, risk factor=0.75 Investment
C: 9% return per year, risk factor=0.40 A client wishes to invest up to $50,000.
He wants an annual return of at least $6300 and at least $10,000 invested in type C investments. How much should be invested in each type to minimize his total risk? (Note: If $20,000 is invested in A, that risk totals 0.50×20000=10000.)

Answer 1

Step-by-step explanation:

We can put up a linear programming problem to reduce overall risk while fulfilling the client's objectives. The decision variables should be defined as follows:

Let x = amount invested in Investment A

Let y = amount invested in Investment B

Let z = amount invested in Investment C

ATQ,

Minimize: 0.50x + 0.75y + 0.40z

Subject to the following constraints,

1. Total investment should not exceed $50,000: x + y + z ≤ 50,000
2. The annual return should be at least $6,300: 0.12x + 0.15y + 0.09z ≥ 6,300
3. At least $10,000 should be invested in type C investments: z ≥ 10,000

We also need to consider non-negativity constraints:

x ≥ 0, y ≥ 0, z ≥ 0

Optimal solution:

x = 20,000

y = 20,000

z = 10,000

Therefore, to minimize the total risk while meeting the client's requirements, the client should invest $20,000 in Investment A, $20,000 in Investment B, and $10,000 in Investment C.