Union Bank wishes to maximize a block of assets equaling exist500,000 by investi
ID: 3854594 • Letter: U
Question
Union Bank wishes to maximize a block of assets equaling exist500,000 by investing in bonds, home mortgages, car loans, and personal loans. The details of the asset allocation and returns are in the table below. Also, personal loans cannot be more than 25% of the total investment amount. In addition, bond investment must be equal or more than personal loans, as well as, home mortgages investment must be equal to or more than personal loans. Using the skills you have learned, create an LP model for the above problem and answer the multiple- choice questions below. (Use scantron for answers) ___________ For Union Bank, the optimum solution and objective function value are Bonds = exist162, 500: Home mortgages = exist162, 500: Car loans = exist162, 500: Personal Loans = exist125,000: Objective function value = exist65, 813 Bonds = exist250,000: Home mortgages = exist250, 500: Car loans = exist0: Personal Loans = exist125,000: Objective function value = exist65,000 Bonds = exist250,000: Home mortgage = exist125,000: Car loans = exist0: Personal Loans = exist125,000: Objective function value = exist51, 250 Bonds = exist325,000: Home mortgages = exist162, 500: Car loans = exist0: Personal Loans = exist125,000: Objective function value = exist51, 250 For Union Bank, (rounding off to three decimal places), which statement below describes the optimum solution's uniqueness and degeneracy? Solution is unique and degenerate Solution is not unique and is degenerate Solution is unique and not degenerate Solution is not unique and not degenerate For Union Bank, the total return is 10.00% 10.25% 8.50% 9.50% For Union Bank, the following constraints are binding Total amount invested, personal loans, and car loans Total amount invested, mortgages, bonds Total amount invested, personal loans, bonds Bonds, personal loans, mortgages For Union Bank, a maximization model, the optimized reduced costs for each investment is equal to 0, which means The optimal decision variable is at its simple lower bound The optimal decision variable is between its lower and upper bounds The optimal decision variable is at its simple upper bound The optimal decision variable is not defined by any of the aboveExplanation / Answer
availability of resources = maximum block of assets = $ 500000
decision variables let
bond investment = x1
home mortages = x2
car loans = x3
personal loans = x4
objective function maximize assets
z= x1 X .100 + X2 X .085 + X3 X .095 + X4 X.125
CONSTRAINTS X4 = 0.25X500000 = $125000
X1 AND X2 GREATER THAN OR EQUAL TO $125000
resources x1 + x2 + x3+ x4= $500000
11. CORRECT ANSWER IS C
as it satisfies the all the constraints and resouces equation
12. CORRECT ANSWER IS A.
AS the solution is unique feasible solution following all the constraints and giving the optimal value of objective function by maximizing the block of investments.
13. . CORRECT ANSWER IS B.
AS THE TOTAL RETURN ON INVESTMENT IS 51250 WHERE
x1 + x2 + x3 + x4 = 250000 + 125000 + 0 + 125000 = 500000
finding the percentage of return y as follows
500000 x y /100 = 51250
y = 51250 x 100 /500000 = 10.25
14. CORRECT ANSWER IS A.
A binding constraint is a constraint which brings the optimal solution to problem
and any changes in its value will bring the change in optimal solution.
hence IF THE VALUE OF TOTAL INVESTMENT AND THE PERCENTAGE OF PERSONAL LOAN CHANGES THE OPTIMAL VALUE OF SOLUTION WILL ALSO CHANGE.
in case of b., c, d options bond and mortages have big range greater than personal loan,which may vary hence in correct opitions
15. correct answer is d.
because in case of a, b, c options,
decison variables are investment value of bonds, mortages , car loan and personal loan, where except car loan rest all can not be zero as per constraint given.
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