Question

The Fiedler family has up to $130,000 to invest. They decide that they want to have at least
$40,000 invested in stable bonds yielding 5.5% and that no more than $60,000 should be
invested in more volatile bonds yielding 11%. How much should they invest in each type of
bond to maximize income if the amount in the stable bond should not exceed the amount in
the more volatile bond? What is the maximum income?

Answer 1

@phi

Answer 2

@mathstudent55

Answer 3

@ganeshie8

Answer 4

this is all i have so far...
x = money invested in stable bonds (5.5%)
y = money invested in volatile bonds (11%) total

z = 0.055x + 0.11y
x + y < 130,000
0.055x + y > 40,000
0.11y + x < 60,000

Answer 5

This is a math problem, it's precalculus, it's a method to find the minimize the cost and maximize profit of something.

Answer 6

we need to follow the following the procedures:

1Choose the unknowns.

2Write the objective function.

3Write the constraints as a system of inequalities.

4 Find the set of feasible solutions that graphically represent the constraints.

5 Calculate the coordinates of the vertices from the compound of feasible solutions.

6 Calculate the value of the objective function at each of the vertices to determine which of them has the maximum or minimum values. It must be taken into account the possible non-existence of a solution if the compound is not bounded.

Answer 7

Corner (x, y) Objective Function "z = 86x + 130y"

(x, y) z = 86(0) + 130(0)
(0, 100) z = 86(0) + 130(100) = $ 13086
(85.56, 0) z = 86(85.56) + 130(0) = $ 7358.16
(0, 110) z = 86(0) + 130(110) = $ 14300
(35, 65) z = 86(35) + 130(65) = $ 11460
(100, 0) z = 86(100) + 130(0) = $ 8600 <----- Minimum cost.

This is an example of another linear programing problem, after we set up the inequality, we will begins to find vertices and substitute x and y axis variables. It is easier to solve rather than yahoo's method.

Answer 8

I have been looking around the internet, i found the correct answer for this question is:

$60,000 in the stable bonds and $60,000 in the volatile bonds; maximum income $9900

Answer 9

I hope you guys can correct my constraints of inequality to see if it is correct or not, i can do the rest. Hope you guys help me. Thank!

x = money invested in stable bonds (5.5%)
y = money invested in volatile bonds (11%) total

z = 0.055x + 0.11y
x + y < 130,000
0.055x + y > 40,000
0.11y + x < 60,000

Answer 10

I am getting below constraints :
z = 0.055x + 0.11y
x + y <= 130,000
x >= 40,000
y <= 60,000
0.055x <= 0.11y

Answer 11

Okay, please hold on, i'm reviewing your constraints, hopefully i will get some ideas. =)

Answer 12

lets keep them even more simpler :

z = 0.055x + 0.11y
x + y <= 130,000
x >= 40,000
y <= 60,000
x <= y

Answer 13

they should work ^^

Answer 14

also, changing the units to thousands simplifies calculations :

z = 0.055x + 0.11y
x + y <= 130
x >= 40
y <= 60
x <= y

Answer 15

Okay, i understand your constraints, i will work on the rest of the problem, and then I'll share with you my graphs and answers... Thanks! I gave you a medal as well. ^ ^

Answer 16

good luck !
you should get the MAXIMUM value for z at x=60, y=60 :
http://www.wolframalpha.com/input/?i=maximize+z+%3D+0.055x+%2B+0.11y%2C+x+%2B+y+%3C%3D+130%2Cx+%3E%3D+40%2C+y+%3C%3D++60%2C+x+%3C%3D+y

Answer 17

Yah, thank you so much for sharing your ideas, and as well as the website you just posted. I see this tool will help me a lot in my studying. I'm sure your answer is correct because i have been looking around the internet for the most reliable answer. And it is "$60,000 in the stable bonds and $60,000 in the volatile bonds; maximum income $9900" ^^

Answer 18

sounds good :) wolfram is your best friend when doing tough problems like these

Answer 19

Thanks! for the medal..

Answer 20

But after i graph this problem, How do i shade it? Which vertices (x,y) do i need to use to test?

Answer 21

@ganeshie8

Answer 22

I know that and the intersection of (60,60) is where the Fiedler family should invest
$60,000 in the stable bonds and $60,000 in the volatile bonds. But we must also use others (x,y) to test to prove that (60,60) is the most profitable.

Answer 23

yes, we need to test all the vertices of common region

Answer 24

graph the inequalities here :
https://www.desmos.com/calculator

Answer 25

I'm seeing 8 points in there, is it necessary to test out 8 points? or we should just pick the relevant one?

Answer 26

dont graph the line,
graph the inequality...

Answer 27

i am getting only 3 points... wait a sec, il attach the graph

Answer 28

Yeah, only 3 points he'll attach a graph

Answer 29

Okay =( I'm waiting patiently.

Answer 30

that triangle is the common region satisfying all the constraints ^^

Answer 31

the maximum value occurs only at the vertices of that triangle

Answer 32

vertices of common region :

(60, 60)
(40, 60)
(40, 40)

Answer 33

so you need to test the "z" at all those 3 points and see which point gives the maximum

Answer 34

Yah, now i get it, your graph looks exactly like mine, how coincident, :P. Okay i will use those 3 points. But May i just shade the triangle instead everything else in different colors?

Answer 35

yes :) geogebra gives more visually pleasing picture... let me attach the graph from geogebra

Answer 36

Okay, you have many secret tools =P.

Answer 37

It seem like i need to download this software before using it. May i ask you if it is trustable?

Answer 38

100% trustable

Answer 39

there is an online version also :
http://www.geogebra.org/webstart/geogebra.html

Answer 40

Yah, I'm testing it now. =)