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, 10% 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: (i)yes (ii) no explain. (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. %
Answers
SORRY I DON'T KNOW!!!!!
Answer:
Linear programming model is mathematical model with linear objective function and a set of a linear constraints and non negative variable. H be the amount allocated home loan. Amount allocated to personal loan. Amount allocated to automobile loans.
(see the first photo attached)
b) use Excel to solve for optimal solution and sensor sensitivity report using the following steps.
1) select the data from the ribbon
2) select solver from the analysis group
3) when the solver parameters dialogue appears enter the objective function
Select the TO: Max Option
Enter the decision variable into by changing variable cells box
Select AJJ
4) when the add constant dialogue box appears and the constant in all the cell reference bar
select <=
Enter the right hand side in the content box.
click OK
5) when the solver parameters dialogue box appears click the checkbox make on constant variable non negative
6) select a solving methods of down button
7) click solve
8) render salwars designs dialogue box select keep solver solution
Select sensitivity in the report box
The optimal solution is equals to 400.000, p = 825000 and A = 375.000 substitute this values into the objective function to find its value
0.07H + 0.12P + 0.09A = 0.07(400.000) + 012(225.000) + 0.09 (375.000)
= 28.000 + 27.000 + 33.750
= 88.750
Annual percentage return is the ratio of the total annual divided by the amount of funds expressed by a percentage
88.75/1.000000 X 100%
= 8.875%
C) sensitivity report created by Excel the object coefficients for Earth is no lower limit 0.101. Since 0.09 is within the optimal solution remains h equals to 400.000, p = 225.000 and 375.000
d) From the sensitivity report created by Excel.The shadow price for the new fund is 0.069. The right hand side for new fund number upper limit then if new fund available in created is 10.000 the shadow price is applicable.
e) the new linear model is as follows :
(see 2nd picture attached below)
see 3rd, 4th and 5th picture attached below)
The answer is too long to type so I wrote it down and attached it below.
