Adirondack Savings Bank (ASB) has $1 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 5% for home loans, 13% for personal loans, and 7% for automobile loans. The bank's planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated personal loans cannot exceed 60% of the amount allocated to automobile loans. (a) Formulate a linear programming model that can be used to determine the amount of funds ASB should allocate to each type of loan to maximize the total annual return for the new funds. If the constant is "1" it must be entered in the box. If your answer is zero enter "o". Let H = amount allocated to home loans P = amount allocated to personal loans A = amount allocated to automobile loans Max H + A s.t. H + A 2 Minimum Home Loans H + Personal Loan Requirement AS H + A = Amount of New Funds (b) How much should be allocated to each type of loan? Loan type Home Allocation Personal Automobile What is the total annual return? If required, round your answer to nearest whole dollar amount. What is the annual percentage return? If required, round your answer to two decimal places. % (c) If the interest rate on home loans increases to 9%, would the amount allocated to each type of loan change? - Select your answer - Explain. | within the allowable range, so the amount allocated to each type of loan An increase to 9% - Select your answer - |- Select your answer - v change. (d) Suppose the total amount of new funds available is increased by $10,000. What effect would this have on the total annual return? Explain. If required, round your answer to nearest whole dollar amount. An increase of $10,000 to the total amount of funds available would increase the total annual return by $ (e) Assume that ASB has the original $1 million in new funds available and that the planning committee has agreed to relax the requirement that at least 40% of the new funds must be allocated to home loans by 1%. How much would the annual return change? If required, round your answer to nearest whole dollar amount. How much would the annual percentage return change? If required, round your answer to two decimal places.
Adirondack Savings Bank (ASB) has $1 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 5% for home loans, 13% for personal loans, and 7% for automobile loans. The bank's planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated personal loans cannot exceed 60% of the amount allocated to automobile loans. (a) Formulate a linear programming model that can be used to determine the amount of funds ASB should allocate to each type of loan to maximize the total annual return for the new funds. If the constant is "1" it must be entered in the box. If your answer is zero enter "o". Let H = amount allocated to home loans P = amount allocated to personal loans A = amount allocated to automobile loans Max H + A s.t. H + A 2 Minimum Home Loans H + Personal Loan Requirement AS H + A = Amount of New Funds (b) How much should be allocated to each type of loan? Loan type Home Allocation Personal Automobile What is the total annual return? If required, round your answer to nearest whole dollar amount. What is the annual percentage return? If required, round your answer to two decimal places. % (c) If the interest rate on home loans increases to 9%, would the amount allocated to each type of loan change? - Select your answer - Explain. | within the allowable range, so the amount allocated to each type of loan An increase to 9% - Select your answer - |- Select your answer - v change. (d) Suppose the total amount of new funds available is increased by $10,000. What effect would this have on the total annual return? Explain. If required, round your answer to nearest whole dollar amount. An increase of $10,000 to the total amount of funds available would increase the total annual return by $ (e) Assume that ASB has the original $1 million in new funds available and that the planning committee has agreed to relax the requirement that at least 40% of the new funds must be allocated to home loans by 1%. How much would the annual return change? If required, round your answer to nearest whole dollar amount. How much would the annual percentage return change? If required, round your answer to two decimal places.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
Related questions
Concept explainers
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Topic Video
Question
Transcribed Image Text:Adirondack Savings Bank (ASB) has $1 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates
of return for the three types of loans are 5% for home loans, 13% for personal loans, and 7% for automobile loans. The bank's planning committee has
decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to
personal loans cannot exceed 60% of the amount allocated to automobile loans.
(a) Formulate a linear programming model that can be used to determine the amount of funds ASB should allocate to each type of loan to maximize the
total annual return for the new funds. If the constant is "1" it must be entered in the box. If your answer is zero enter "0".
Let H = amount allocated to home loans
P = amount allocated to personal loans
A = amount allocated to automobile loans
Маx
H +
P +
s.t.
H +
A 2
Minimum Home Loans
P +
AS
Personal Loan Requirement
H +
P +
A =
Amount of New Funds
(b) How much should be allocated to each type of loan?
Loan type
Allocation
Home
Personal
Automobile
What is the total annual return?
If required, round your answer to nearest whole dollar amount.
What is the annual percentage return?
If required, round your answer to two decimal places.
%
(c) If the interest rate on home loans increases to 9%, would the amount allocated to each type of loan change?
- Select your answer
Explain.
An increase to 9% - Select your answer - v within the allowable range, so the amount allocated to each type of loan
Select your answer -
change.
(d) Suppose the total amount of new funds available is increased by $10,000. What effect would this have on the total annual return? Explain.
If required, round your answer to nearest whole dollar amount.
An increase of $10,000 to the total amount of funds available would increase the total annual return by $
(e) Assume that ASB has the original $1 million in new funds available and that the planning committee has agreed to relax the requirement that at least
40% of the new funds must be allocated to home loans by 1%. How much would the annual return change?
If required, round your answer to nearest whole dollar amount.
How much would the annual percentage return change?
If required, round your answer to two decimal places.
%
Expert Solution
Trending now
This is a popular solution!
Step by step
Solved in 9 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning