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

@jim_thompson5910

Answer 2

first define your variables

let

x = amount of money (in dollars) invested in the stable bonds at 5.5%

y = amount of money (in dollars) invested in the volatile bonds at 11%

Answer 3

They have up to $130,000 to invest, so this means that the total they have to invest cannot be larger than 130,00

so this means

total <= 130000

x+y <= 130000

since x+y is the total amount to invest (in both combined)

Answer 4

stable bonds = 130.000 - 60,000 = 70,000

Answer 5

we're also told that "they want to have at least $40,000 invested in stable bonds yielding 5.5%", so we know

x >= 40000

and we're given that "no more than $60,000 should be invested in more volatile bonds yielding 11%", so we can say

y <= 60000

Answer 6

volatile bonds = not > than 60,000

Answer 7

ok

Answer 8

with me so far?

Answer 9

yes @jim_thompson5910

Answer 10

what you do from here is you graph each inequality on the same xy plane

Answer 11

then make notes where the points of intersections are between each line

Answer 12

to help define the feasible region

Answer 13

um okl

Answer 14

do you know how to do that?

Answer 15

let me see

Answer 16

ok i did it all and i got

Answer 17

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

Answer 18

let me check

Answer 19

k

Answer 20

what points of intersection did you get

Answer 21

OMG MY BATTERY IS ABOUT DIE THANK YOU SO SO SO MUCH FOR YOUR HELP THUS FAR @jim_thompson5910

Answer 22

hopefully you can grab a charger and an outlet

Answer 23

but basically you use the points of intersection and you plug them into 0.055x + 0.11y to determine which yields the max return

Answer 24

IM ON A PLAN SO NOO OUTLETS

Answer 25

PLANE

Answer 26

oh gotcha, then perhaps when you land is a good time to work on this

Answer 27

OK YEAH GREAT IDEA ;-)

Answer 28

@jim_thompson5910 i need your help with this same problem.