SOLUTION: Need assistance please. I really don't know what I am doing, and the book only provides one (poor) example.
Solve using the graphical method. Choose your variables, write the
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Question 1129079: Need assistance please. I really don't know what I am doing, and the book only provides one (poor) example.
Solve using the graphical method. Choose your variables, write the objective function and the constraints, graph the constraints, shade the feasibility region, label all corner points, and determine the solution that optimizes the objective function.
Problem is as follows:
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?
What I have done:
Choose variables-
X=amount invested in bonds
y=amount invested in stocks
Objective function-
P=.06x+.08y
Constraints-
This is what I am struggling with most. I find it hard to pull these out of the word problem. What I have is:
x+y>=24,000
x<=18,000
What I'm really struggling with is where this sentence, "money invested in bonds must be at least twice as much as that in stocks" fits into the equation.
If anyone has an god advice on how to set up an equation such as this I would sure appreciate it.
Thank you!
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!
You've done such a good job on what you have done; I'm surprised that the last constraint has you confused.
You said x = amount invested in bonds and y = amount invested in stocks. Using those directly, the constraint
"the money invested in bonds must be at least twice as much as that in stocks"
is
x >= 2y
Note also that your constraint on the total amount should be x+y <= 24000; you show x+y >= 24000. I don't know if you really meant that, or if it was a typo.
Other than that, I suspect you are capable of finishing the problem. If not, send a note of thanks indicating where you are stuck and I can help further.
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
.
To get more confidence in solving such problems, you simply need to see more samples/examples of solved problems.
Look into the lesson
- Solving minimax problems by the Linear Programming method
in this site.
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