In: Statistics and Probability
Adirondack Savings Bank (ASB) has $1 million in new funds that
must be allocated to home...
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
7% for home loans, 11% 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 |
|
|
Max |
____ H |
+ |
____ P |
+ |
____ A |
|
|
|
s.t. |
|
|
|
|
|
|
|
|
|
____ H |
+ |
____P |
+ |
____A |
≥ |
_____ |
Minimum Home Loans |
|
____H |
+ |
____P |
+ |
____A |
≤ |
_____ |
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 -Yes or No |
|
|
(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. |
|
%____? |