Question

An investor has 75,000 to invest in a CD and a mutual fund. The CD yields 6​% and the mutual fund yields 8%. The mutual fund requires a minimum investment of $8,000​, 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

Answer:

investment in cd = x  = $50000

investment in mutual funds  = $ 25000

return = $5000

Step-by-step explanation:

let x be the investment in CD

let y be in mutual fund

from the data given we have

Return  = 6% x + 8% y

Return = 0.06 x + 0.08 y

$y \geq  8000$

$x \geq 2y$

$x + y \leq 7500$

plotting these three inequalities on graph  we have 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 maximum benefit is $5000 so we have

investment in cd = x  = $50000

investment in mutual funds  = $ 25000

return = $5000

Answer 2

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;

$y\geq 8000\\\\x\geq 2y\\\\x+ y \leq 7500$

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

Learn more about inequality ;

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