A couple has up to $30,000 to invest in mutual funds. The broker recommends inve

Question

A couple has up to $30,000 to invest in mutual funds. The broker recommends investing in
                    two funds based on their average annual return for the 5 years ending in December, 2012: the Xander
                    Global Bond fund yielding 8% and the Yoren International Cap Growth fund yielding 12%. After
                    some consideration the couple decides to invest at most $12,000 into the Yoren International Small
                    Cap Growth fund and at least $6,000 in the Xander Global Bond fund. They also want the amount
                    invested in the Xander Global fund to exceed or equal the amount invested in the Yoren International
                    Small Cap Growth fund. What should the broker recommend if the couple wants to maximize the
                    return on their investment?

Explanation / Answer

Let us make the following assumptions:

amount invested in Xander global bond fund = X1

amount invested in Yoren international cap growth fund = X2

As per the question, X1 >= $ 6000 and X2 =< $12000 and X1 >= X2 (or, X1 - X2 >= 0)

Also, X1+ X2 =< $30000 (max. money that the couple has for investment)

Return on investment will be (0.08*X1 + 0.12*X2) which needs to be maximised.

Further contraints: X1 , X2 >= 0 (positive values)

Using Linear programing calculator (http://www.zweigmedia.com/RealWorld/simplex.html):

Optimal Solution: Maximum Return on Investment = $2880;

X1 = $18000,

X2 = $12000

Thus, amount invested in Xander global bond fund = $18000

amount invested in Yoren international cap growth fund = $12000

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