an investor is considereing three types of investment: a high-risk venture into oil leases with a potential return of 15%, a medium risk investment in bonds with a 9% return, and a relatively safe stock investment with a 5% return. He has $50,000 to invest. Because of the risk; he will limit his investment in oil leases and bonds to 30% and his investment in oil leases and stock to 50%. How much should he incest in each to maximize his returns assuming investment returns are as expected?
To determine how much the investor should invest in each type of investment to maximize his returns, we can use linear programming. Here's how we can approach it:
1. Assign variables: Let's assign three variables to represent the amount of money the investor will invest in each type of investment. Let's say x represents the amount invested in oil leases, y represents the amount invested in bonds, and z represents the amount invested in stocks.
2. Define the objective function: The objective is to maximize the returns. The returns can be calculated as follows:
Return = 0.15x + 0.09y + 0.05z
3. Set up constraints: The investor has three constraints based on the risk limits:
- The investment in oil leases and bonds should not exceed 30% of the total investment, i.e., x + y ≤ 0.3($50,000)
- The investment in oil leases and stocks should not exceed 50% of the total investment, i.e., x + z ≤ 0.5($50,000)
- The total investment should not exceed the available $50,000, i.e., x + y + z ≤ $50,000
4. Non-negativity constraint: Since the investment amount cannot be negative, x, y, and z should be greater than or equal to zero.
Now, we have our objective function and constraints, and we can solve this linear programming problem using optimization techniques available in various software or programming languages.
The solution to this problem will provide the ideal investment amount in each type of investment to maximize returns.