1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ankoles [38]
3 years ago
12

Madison Finance has a total of $22 million earmarked for homeowner loans and auto loans, where x is homeowner loans in millions

of dollars and y is auto loans in millions of dollars. On the average, homeowner loans have a 8% annual rate of return, whereas auto loans yield a 13% annual rate of return. Management has also stipulated that the total amount of homeowner loans should be greater than or equal to 4 times the total amount of automobile loans. Determine the total amount of loans of each type Madison should extend to each category to maximize its returns P in millions of dollars.Maxmize P=total loansdistributtion of loans
Mathematics
1 answer:
erik [133]3 years ago
7 0

Answer:

Maximum returns = $1,980,000

x = Homeowner loans = $17,600,000

y = Auto loans = $4,400,000

Madison should extend $17,600,000 in home owners loans and $4,400,000 in auto loans in order to have a maximum return of $1,980,000

Step-by-step explanation:

From the question we are told that:

Madison Finance has a total of $22 million earmarked for homeowner loans and auto loans, where x is homeowner loans in millions of dollars and y is auto loans in millions of dollars.

On the average, homeowner loans have a 8% annual rate of return, whereas auto loans yield a 13% annual rate of return.

We have the equation:

Maximum Return = 8% × x + 13% × y

= 0.08x + 0.13y

We are told in the question that

Management has also stipulated that the total amount of homeowner loans should be greater than or equal to 4 times the total amount of automobile loans.

Hence,

x ≥ 4y

So:

x + y = $22,000,000

4y + y = $22,000,000

5y = $22,000,000

y = $22,000,000/5

y = 4,400,000

x = 4y

x = 4(4,400,000)

x = 17,600,000

Maximum Return = 0.08x + 0.13y

= 0.08 × 17,600,000 + 0.13 × 4,400,000

= $1,980,000

Therefore, Madison should extend $17,600,000 in home owners loans and $4,400,000 in auto loans in order to have a maximum return of $1,980,000

You might be interested in
Can someone help me?
AfilCa [17]

Answer: 14450

Step-by-step explanation:

15% of 17000 is 2550. 17000-2550 is 14450

4 0
2 years ago
Hey scale drawing of Jamy’s living room is 4cm in width and 6cm length. If each 2cm on the scale drawing equals 8 feet what are
igor_vitrenko [27]
2 cm = 8 feet.
4 / 2 = 2. 8 * 2 = 16.  16 feet in width.
Now, the length:
6 / 2 = 3. 8 * 3 = 24. 24 feet in length.
The actual dimensions are 16 feet in width and 24 feet in length.

5 0
3 years ago
The sum of 27 and seven times a number is 125. Find the number.
zysi [14]
The number is 14

Here's the solution:

Let the number be x

According to the question,

27+7x=125

//Subtract 27 from both the sides

7x=125-27

7x=98

//divide both the sides by 7

x=98/7

x=14
9 0
3 years ago
Read 2 more answers
Two problems I can’t get is; 94-4.8 I know the answer is 89.2 but how?
vekshin1

Answer:

have the correct answer

Step-by-step explanation:

a-line the decimals nd subtract

6 0
3 years ago
If 3x - 8= -2, find the value of x - 6.
siniylev [52]

Answer:

x-6 = -4

Step-by-step explanation:

3x - 8= -2

Add 8 to each side

3x - 8+8= -2+8

3x = 6

Divide by 3

3x/3 = 6/2

x =2

We want to find x-6

2-6 = -4

4 0
2 years ago
Read 2 more answers
Other questions:
  • A polynomial expression is shown below.
    13·1 answer
  • The perimeter of Dawna's new flat screen television is 112 inches. The ratio of its length to width is 4:3. Write and solve an a
    12·1 answer
  • PLEASE HELP !
    14·2 answers
  • Twenty is no greater than the sum of a number and -4.
    8·1 answer
  • Find the sum of the given vectors and illustrate geometrically. [-2,-1],[5,7]
    11·1 answer
  • If two squirrels live in one square meter of a fifty square meter park what is the park's estimated squirrel population?
    5·2 answers
  • Write 2.789 in word form
    13·2 answers
  • At a sale, dresses were sold for $22 each. This price was 55% of a dress's original price. How much did a dress originally cost?
    5·2 answers
  • What is the image of (-4,2) after a reflection over the y-axis (PLEASE SHOW STEPS PLEASE I REALLY NEED IT ASAP )
    15·1 answer
  • The points (–7, 7) and (6, –6) fall on a particular line. What is its equation in slope-intercept form?
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!