Suppose that you inherit $11 comma 00011,000. The will states how you must inves

Question

Suppose that you inherit

$11 comma 00011,000.

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

$0.050.05

per dollar, and at least

$20002000

be invested in stocks, with expected returns of

$0.080.08

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 $___ in bonds and $___ in stock.

Explanation / Answer

If x and y are the amounts of investment in bonds and stocks respectively,
Maximize { Expected_Return = 0.05x + 0.08y },
x + y 11000 (inherited sum);
x 3000 (at least); y 2000 (at least);
x y (final requirement)

Marking the graph yourself -

the domain is a quadrilateral in the 1st quadrant with 2 right angles and vertices (3000, 2000), (3000, 3000), (5000, 5000) and (8000, 2000).

The maximal object function value is attained in the 3rd listed vertex, so the optimal solution is
x = y = 5000; Max_Return = 1000

i think it is not a bad investment right

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