Suppose that portfolios I and II in Problem 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?
To determine how many units of each portfolio should be offered, we need to solve a system of equations. Let's denote the number of units of portfolio I, II, and III as x, y, and z respectively.
From the information given, we can form the following equations:
For common stock: x + 3z = 12
For municipal bonds: 2z = 6
For preferred stock: y + 2z = 6
Let's solve this system of equations:
From equation 2, we get z = 3.
Substituting z = 3 into equation 1, we get x + 9 = 12. Solving for x, we get x = 3.
Substituting z = 3 into equation 3, we get y + 6 = 6. Solving for y, we get y = 0.
So, we need to offer 3 units of portfolio I, 0 units of portfolio II, and 3 units of portfolio III to meet the customer's requirements.