50 POINTS! You have $10,000 to invest, and three different funds from which to choose. The municipal bond fund has a 7% return, the local bank's CDs have an 8% return, and the high‐risk account has an expected (hoped‐for) 12% return. To minimize risk, you decide not to invest any more than $2,000 in the high‐risk account. For tax reasons, you need to invest at least three times as much in the municipal bonds as in the bank CDs. Assuming the year‐end yields are as expected, what are the optimal investment amounts?

Optimal investment amount = $300

Step-by-step explanation:

discount = x

original price = 10,000

discount% = 7%

x/10,000 = 7/100

x · 100 = 7 · 10,000

100x = 70,000

100x/100 = 70,000/100

x = 700

discount = x

original price = 10,000

discount% = 8%

x/10,000 = 8/100

x · 100 = 8 · 10,000

100x = 80,000

100x/100 = 80,000/100

x = 800

discount = x

original price = 10,000

discount% = 12%

x/10,000 = 12/100

x · 100 = 12 · 10,000

100x = 120,000

100x/100 = 120,000/100

x = 1,200

So:

$1,200 - $800 - $700 = $300

We max out the high return investment, $2000 for 12%.

We have $8000 left to invest and we want to put as much in CDs at 8% as possible.  Let's call b the bond investment and c the CD investment.  We have

b ≥ 3c

Since munis have the lower return we want as many CDs as possible.  So we choose:

b = 3c

b + c = 8000

3c + c = 8000

4c = 8000

c = 2000

That leaves b=3c=6000 for bonds.

$6000 in bonds, $2000 in CDs, $2000 in high-risk.

answer: hi

step-by-step explanation:

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet