Mr. and Mrs. Garcia have a total of $100,000 to be invested in stocks, bonds, and a money market account. The stocks have a rate of return of 12%/year, while the bonds and the money market account pay 8%/year and 4%/year, respectively. The Garcias have stipulated that the amount invested in stocks should be equal to the sum of the amount invested in bonds and 3 times the amount invested in the money market account. How should the Garcias allocate their resources if they require an annual income of $10,000 from their investments

Explanation:

Let y amount be invested in bonds

Let x amount be invested in money account

Let x amount be invested in stocks

x = y + 3x

10,000 = 12/100(y+3x) + 8/100*y + 4/100*x

10,000 = 12(y+3x) + 8y + 4x / 100

10,000 * 100 = 12y+36x + 8y + 4x

2500 * 100 = 3y + 9x + 2y + x

250,000 = 5y + 10x

50,000 = y + 2x(1)

x + y + z = $100,000

y + 3x + y + x = $100,000

2y + 4x = 100,000

y + 2x = 50,000(ii)

y = 50,000 - 2x

x = 50,000 + x

z = z

2 Options are

{(x,y,x), (x2,y2,z2)}

= (50000, 50000) (60000, 30000, 10000)

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