Adirondack Savings Bank (ASB) has $1 million in new funds thatmust be allocated to home loans, personal loans, and automobileloans. The annual rates of return for the three types of loans are5% for home loans, 13% for personal loans, and 8% for automobileloans. The bank’s planning committee has decided that at least 40%of the new funds must be allocated to home loans. In addition, theplanning committee has specified that the amount allocated topersonal loans cannot exceed 60% of the amount allocated toautomobile loans.
| (a) | Formulate a linear programming model that can be used todetermine the amount of funds ASB should allocate to each type ofloan to maximize the total annual return for the new funds. If theconstant is \"1\" it must be entered in the box. If your answer iszero enter “0â€. |
| | Let | H | = | amount allocated to home loans | | P | = | amount allocated to personal loans | | A | = | amount allocated to automobile loans |
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| | 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 |
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| (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 dollaramount. |
| $ |
| What is the annual percentage return? |
| If required, round your answer to two decimal places. |
| % |
| (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 dollaramount. |
| An increase of $10,000 to the total amount of funds availablewould increase the total annual return by $ . |
| (e) | Assume that ASB has the original $1 million in new fundsavailable and that the planning committee has agreed to relax therequirement that at least 40% of the new funds must be allocated tohome loans by 1%. How much would the annual return change? |
| If required, round your answer to nearest whole dollaramount. |
| $ |
| How much would the annual percentage return change? |
| If required, round your answer to two decimal places. |
| % |
