Problema Solution
An investor has $70 comma 00070,000 to invest in a CD and a mutual fund. The CD yields 88% and the mutual fund yields 55%. The mutual fund requires a minimum investment of $10 comma 00010,000, and the investor requires that at least twice as much should be invested in CDs as in the mutual fund. How much should be invested in CDs and how much in the mutual fund to maximize the return? What is the maximum return?
Answer provided by our tutors
Let
x = the amount invested in CDs, x>=0
y = the amount invested in mutual fund, y>= 0
x + y = 70,000
y >= 10,000
x >= 2y
The objective function is: F(x , y) = 0.88x + 0.55y
We need to find the corner point of:
x + y <= 70,000
y >= 10,000
x >= 2y
x >= 0
y >= 0
The corner points are (20000, 10000), (60000, 10000), (46667, 23333):
F(20000, 10000) = 0.88*20000 + 0.55*10000 = 23,100
F(60000, 10000) = 0.88*60000 + 0.55*10000 = 58,300
F(46667, 23333) = 0.88*46667 + 0.55*23333 = 53,900
The maximum return is $58,300.
$60,000 is invested in CDs and $10,000 is invested in mutual fund.