Mr. Tran has $24,000 to invest, some in bonds and the rest in stocks. He has decided that the money invested in bonds must be at least twice as much as that in stocks. But the money invested in bonds must not be greater than $18,000. If the bonds earn 6%, and the stocks earn 8%, how much money should he invest in each to maximize profit?

The maximize profit for is bond is $18000.

The maximize profit for stocks is $6000

Suppose that ; Mr. Tran invested x amount in bonds and y amount in stocks.

According to given question;

The bonds earn 6% and stocks earn 8% profit ,

Then profit could be ,

P = 0.06 + 0.08

Total amount = $24,000

So, the equation can be return as

x + y = $24000

The money invested in bonds at least twice the equation can be return as

the money invested in the bonds not greater than will be

The linear programming would be  shown below  

By the graphical method maximize the profit .

The critical points shown in the attached image is ($6000,$18000) & ($16000,$18000)

Thus the maximize profit for bond is $18000

The maximize profit for stocks is $6000.

For more details follow the link given below

For bond it is $16,000

And, for stocks it is $8,000

Step-by-step explanation:

Let us assume the Tran invested x amount in bonds and y amount in stocks

So, the profit could be

P = 0.06x + 0.08y

The total amount is $24,000

so, the equation would be

x + y = $24,000

Now in the case of atleast twice, the equation would be

x ≥ 2y

And, in the case of not be greather than $18,000, the equation would be

x ≤ $18,000

The linear programming problem would be shown below:

maximum P = 0.06x + 0.08y

subjected to

x + y = $24,000

x ≥ 2y

x ≤ $18,000

x ≥0, y ≥0

Now use the graphical method, the critical point is ($18,000,$6,000) or ($6,000, $18,000)

In the case when we have to maximise the profits

For bond it is $16,000

And, for stocks it is $8,000

step-by-step explanation:

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step-by-step explanation: