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Suppose that you inherit​$10 comma 00010,000.The will states how you must invest the money. Some​ (or all) of the money must be invested in stocks and bonds. The requirements are that at least​$30003000be invested in​ bonds, with expected returns of​$0.140.14per​ dollar, and at least​$20002000be invested in​ stocks, with expected returns of​$0.190.19per dollar. Because the stocks are medium​ risk, the final stipulation requires that the investment in bonds should never be less than the investment in stocks. How should the money be invested so as to maximize your expected​ returns?To maximize the expected​ returns, invest​$60006000in bonds and​$60006000in stocks.

Question
Suppose that you inherit
​$10 comma 00010,000.
The will states how you must invest the money. Some​ (or all) of the money must be invested in stocks and bonds. The requirements are that at least
​$30003000
be invested in​ bonds, with expected returns of
​$0.140.14
per​ dollar, and at least
​$20002000
be invested in​ stocks, with expected returns of
​$0.190.19
per dollar. Because the stocks are medium​ risk, the final stipulation requires that the investment in bonds should never be less than the investment in stocks. How should the money be invested so as to maximize your expected​ returns?
To maximize the expected​ returns, invest
​$60006000
in bonds and
​$60006000
in stocks.
check_circleAnswer
Step 1

Note: Here we have considered that “$10 comma 00010,000 , $30003000, $0.140.14, ​$20002000, ​$0.190.19” are repeated twice.

Suppose that you inherit $10000. The will states that you  must invest the money (some or all) in stocks and bonds. The requirements are at least $3000 in bond and $2000 in stocks with expected returns of $0.14 per dollar and $0.19 per dollar respectively.

Since, the stocks are medium​ risk, the final stipulation requires that the investment in bonds should never be less than the investment in stocks. 

Step 2

Let x be the amount invested in bond and y be the amount invested in stocks.

So, the expected returns, ER = 0.14x + 0.19y.

And the above conditions are formulated as
x 2 3000
y 2000
x 2 y
And xy 10000
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And the above conditions are formulated as x 2 3000 y 2000 x 2 y And xy 10000

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Step 3

If we draw the above inequa...

X
x 3000 0x 10000}{0 <y<10000}
X
-10000
y 2000 0x10000 }{0<y1000}
-3000
Xay
x+yc10000
x2y0x10000) {0sys 10000}
X
(xy)
10000 0*s 10000}{0£ys100
15000, 5000)
-5000
(3000, 3000)
X
(8000, 2000) y2000
(3000,
5000
10000
X
help_outline

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X x 3000 0x 10000}{0 <y<10000} X -10000 y 2000 0x10000 }{0<y1000} -3000 Xay x+yc10000 x2y0x10000) {0sys 10000} X (xy) 10000 0*s 10000}{0£ys100 15000, 5000) -5000 (3000, 3000) X (8000, 2000) y2000 (3000, 5000 10000 X

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