Suppose that portfolios I and II in Prob- lem 58 are unchanged and portfolio III consists of 2 blocks of common stock, 2 municipal bonds, and 3 blocks of preferred stock. A customer wants 12 blocks of common stock, 6 municipal bonds, and 6 blocks of preferred stock. How many units of each portfolio should be offered?

Question

Suppose that portfolios I and II in Prob- lem 58 are unchanged and portfolio III consists of 2 blocks of common stock, 2 municipal bonds, and 3 blocks of preferred stock. A customer wants 12 blocks of common stock, 6 municipal bonds, and 6 blocks of preferred stock. How many units of each portfolio should be offered?

Answer 1

Suppose that portfolios I and II in Prob- lem 58 are unchanged and portfolio III consists of 2 blocks of common stock, 2 municipal bonds, and 3 blocks of preferred stock. A customer wants 12 blocks of common stock, 6 municipal bonds, and 6 blocks of preferred stock. How many units of each portfolio should be offered?

Answer 2

Suppose that portfolios I and II in Prob- lem 58 are unchanged and portfolio III consists of 2 blocks of common stock, 2 municipal bonds, and 3 blocks of preferred stock. A customer wants 12 blocks of common stock, 6 municipal bonds, and 6 blocks of preferred stock. How many units of each portfolio should be offered?

Answer 3

To determine how many units of each portfolio should be offered to meet the customer's requirements, we need to solve a system of equations.

Let's represent the unknown number of units of Portfolio I, Portfolio II, and Portfolio III as x, y, and z respectively.

The requirements of the customer are as follows:
- 12 blocks of common stock
- 6 municipal bonds
- 6 blocks of preferred stock

From Problem 58, we know the composition of each portfolio:

Portfolio I consists of:
- 4 blocks of common stock
- 2 municipal bonds
- 3 blocks of preferred stock

Portfolio II consists of:
- 1 block of common stock
- 1 municipal bond
- 5 blocks of preferred stock

Portfolio III consists of:
- 2 blocks of common stock
- 2 municipal bonds
- 3 blocks of preferred stock

We can now set up the equations based on the customer's requirements:

12x + 1y + 2z = 12 (equation for common stock)
2x + 2y + 2z = 6 (equation for municipal bonds)
3x + 5y + 3z = 6 (equation for preferred stock)

Now, we can solve this system of equations for x, y, and z using any suitable method such as substitution, elimination, or matrix methods.

Once the values of x, y, and z are obtained, we will have the number of units of each portfolio that should be offered to the customer.