Question

Problem 4-03 (Algorithmic) The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk-free securities to stabilize income. The various revenueproducing investments together with annual rates of return are as follows: Type of Loan/Investment Annual Rate of Return (%) Automobile loans Furniture loans Other secured loans Signature loans Risk-free securities 8 10 12 The credit union wil have $2.4 million available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments Risk-free securities may not exceed 30% of the total funds available for investment . Signature loans may not exceed 10% of the funds invested in all loans automobile, furniture other secured and signature as Furniture loans plus other secured loans may not exceed the automobile loans. Other secured loans plus signature loans may not exceed the funds invested in risk-free securities How should the $2.4 million be allocated to each of the loan/investment alternatives to maximize total annual return? Round your answers to the nearest dollar Automobile Loans Furniture Loans Other Secured Loans$ Signature Loans Risk Free Loans What is the projected total annual return? Round your answer to the nearest dollar

Answer 1

formulating and solving using excel solver

Let A,F,O,S,R represent the allocation for different type of loans named after their first letter Total return will then be 0.08A 0.10F 0.110 0.12S+0.09R (this is the return that we have to maximize) We have certain conditions (constraints) stated in the problem that need to be satisfied Thus Max. 0.08A+0.10F 0.110 0.12S 0.09R Subject to I) risk free securities allocation not to exceed 30% of total available funds 0.30*2.4 0.10* (A+F+0+5) signature laons not to exceed 10% of the funds invested in all loans furniture and other secured not to exceed automobile loans other secured and signature not to exceed funds in risk free securities total available funds V) A+F+O+S+R-2.4 This is the Linear Programming Problem we have to solve to get the solution

we type in the formula for return and total followed by providing return as objective to be maximized. Then, giving the constraints as shown below, choosing simplex method and checking non negative variable option.

Solver Parameters -0.08*D5+0.1*E5+0.11*F5+0.12"G5+0.09"H5 Set Objective: SKS6 Max Yalue of By Changing Variable Cells: SD$5:$HSS 0 0 Total Investment 0 Return Subject to the Constraints: 0 SH$S 0.72 SK$524 A+F+0+S Beset All Load/save Make Unconstrained Variables Non-Negative Select a Solving Options Method Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are Close

clicking on solve, we get

Thus, total annual return is $226,560 (Note: All the above figures are in million USD)

Total Investment Return F+O O+S A+F+O+S 0.756 0.2040.552 0.168 0.72 2.4 0.22656 0.756 0.72 1.68