Question

An investor has $75,000 to invest in a CD and a mutual fund. The CD yields 6% and the mutual fund yields 7%.

The mutual fund requires a minimum investment of $10,000, 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 1

The investment in cd would be $50000. the investment in mutual funds would be $ 25000. The maximum return is $5000.
What is inequality?
Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Let x be the investment in CD
Let y be in mutual fund
Given;
Return = 6% x + 8% y
Return = 0.06 x + 0.08 y
The equation form;

we have a critical number as
(16000, 8000) :
return = 0.06 (16000 + 0.08 (8000) = $1600
(50000, 25000) :
return = 0.06 (50000) + 0.08 (25000) = $5000
(67000, 8000)
return = 0.06 (67000) + 0.08(8000) = $4660
As we can see the maximum benefit is $5000 so;
The investment in cd = x = $50000
The investment in mutual funds = $ 25000
The maximum return = $5000