Question

a brokerage house offers three stock portfolios. portfolio a 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 21 blocks of common stock, 10 municipal bonds, and 9 blocks of preferred. stock. how many units of each portfolio should be offered?

Answer 1

x of portfolio 1
y of portfolio 2
z of portfolio 3
portfolio 1: 2 common stock, 1 muni bond
portfolio 2: 4 common stock, 2 muni bond, 3 preferred stock
portfolio 3: 7 common stock, 3 muni bond, 3 preferred stock
so
common 21 = 2 x + 4 y + 7 z
muni 10 = 1 x + 2 y + 3 z
preferred 9 = 3 y + 3 z or 3 = y+z
so
z = (3-y)

21 = 2x + 4 y + 7(3-y)
10 = 1x + 2 y + 3(3-y)

0 = 2 x - 3 y so x = 1.5 y
10 = 1.5 y + 2 y + 9 - 3 y
1 = .5 y
y = 2
go back and get x and z

Answer 2

4,6