An individual wishes to invest $5000 over the next year in two types of investment: investment a yields 5%, and investment b yields 8%. market research recommends an allocation of at least 25% in a and at most 50% in b. moreover, investment in a should be at least half the investment in b. how should the fund be allocated to the two investments?

The amount invested at Investment A must be greater than or equal to $2,750

The amount invested at Investment B must be less than or equal to $2,250

Step-by-step explanation:

Let

x -----> the amount invested at Investment A yields 5%

y -----> the amount invested at Investment B yields 8%

we know that

 -----> equation A

-----> inequality B

-----> inequality C

-----> inequality D

Substitute equation A in the inequality D and solve for y

Multiply by 2 both sides

Multiply by -1 both sides

Adds y both sides

adds 10,000 both sides

Divide by 3 both sides

-----> inequality E

therefore

Solve for y

we have

-----> inequality C

-----> inequality E

The solution of inequality C and inequality E is

For y=2,250

x=5,000-y ----> x=5,000-2,250=2,750

so

-----> inequality F

Solve for x

we have

-----> inequality B

-----> inequality F

The solution of inequality B and inequality F is

therefore

The amount invested at Investment A must be greater than or equal to $2,750

The amount invested at Investment B must be less than or equal to $2,250

-7

step-by-step explanation:

x^2 + 18x + 74 = (x + 9)^2 - 81 + 74

= (x + 9)^2 - 7.

so q = -7.

(x, y)→(x − 8, y − 7)

step-by-step explanation:

enjoy!