A brokerage house offers three stock portfolios. Portfolio I consists of 2 blocks of common stock and 1 municipal bond. Portfolio II consists of 4 blocks of common stock, 2 municipal bonds, and 3 blocks of preferred stock. Portfolio III consists of 7 blocks of common stock, 3 municipal bonds, and 3 blocks of preferred stock. A customer wants blocks of common stock, municipal bonds, and blocks of preferred stock. How many units of each portfolio should be offered?

Question

A brokerage house offers three stock portfolios. Portfolio I consists of 2 blocks of common stock and 1 municipal bond. Portfolio II consists of 4 blocks of common stock, 2 municipal bonds, and 3 blocks of preferred stock. Portfolio III consists of 7 blocks of common stock, 3 municipal bonds, and 3 blocks of preferred stock. A customer wants  blocks of common stock,  municipal bonds, and  blocks of preferred stock. How many units of each portfolio should be offered? ​

Quizplus · Accepted Answer

Let the number of units of each portfolio be x, y, z respectively. Then we have the following system of equations:

2x + 4y + 7z = 11
x + 2y + 3z = 11
y + 3z = 11

Solving for x, y, and z, we get:
x = 1
y = 2
z = 3

Therefore, the customer should be offered 1 unit of Portfolio I, 2 units of Portfolio II, and 3 units of Portfolio III, which corresponds to choice C.

A Brokerage House Offers Three Stock Portfolios