Question

Problem 4-03 (Algorithmic) The employer 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 af Laan/Investment Annual Rate af Retum (%) Automobile loans Furniture Inans 1 Other secured loans Signature loans Risk free securities 4 13 9 The credit union will have $1.4 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 loans). • Furniture loans plus other secured loans may not exceed the automobile loans. . Other secured loans plus signatureloars may not excond the funds invested in risk-free securities. How should the $1.4 million be allocated to each af the laan/'investment alternatives to maximize tatal annual return? Round your answers to the nearest callar. Automobile Loans Furniture Loans Other Secured Loans $ Signature Loans $ 140,000 Risk Free Loans What is the projected total annual return? Round your answer to the nearest dollar. Feedback Cho My Work Incorrect

If you can provide, steps using excel for future questions, it would be greatly appreciated.

Answer 1

Answer Given that Type of loan Invertment | Annual Rate of Retuintay Automobile leane Furniture loans Other secured loans signature loans Risk-free securities CS Scanned with CamScanner

* Let → The amount Inverted an automile I loons 1. be (21) » The amount inversted in furniture loans - be (x2) → The amocent inversted in other second loans be (23) → The amount inversted in a greature lang be (x4) → The amount inverted in sigurature Risk-free securitill be (x5) * Maximize (z) 8% (21) +12% (x2)+14%. (x3) +137-(44) +9%(25) 0.821 +0.1242 +0:1423+0.1374 +0.975 Then X4+22+23+24+75 = 17,00,000 252 309 0f 17,00,000 CS Scanned with 0.8 21+0.1212 +0.1473 +0.1374 +0.925 CamScanner = 17,00,000

o Gunt22623 + zut&s_ = 17,0,000 t 0.8+0:12+0.144+0.13-0.9 - 17.00 PO 2.091 = 17,00,000 B0% = 17,00,000 25% 30% of 1700,000 25+ 30 x 17,00,000 25% 0.2 x 17,00,000 252 510000 > Sigraetere loang may not exceed 10% in all loans of the founds inversted Taue 10% (auth2 +23+14) ² furniture Loans and secured loans maynot exceed the automobile loans TX2443581 F B other secured loans plus signature loans may not exceed the funds Inverted in risk free securities | 23+24=25 / Scanned with CamScanner

* The above constraints are 21 +82 +23 +74+25 = 17,00 p01) — 35 = 5,10,000 - 9 44 = 10% (x1+x8+23+74) — X2+13=31 13+1 =15 - 3 (213 +34 = (510,000) {* *5=510 po] Then substitute the X3+84 Eetr values in Equatlon © 21+12 +5,10,000 + 510,000 =17,00,000 x1+x2 +10,20,000 = 17,00,000 x1tr2 = 17,00,000 –10,20,000 Xi+X2 = 6,80,000 » Then substitute the art22) & (23+84) Values in equation ③ 24 = 10% (680,000 +5,10,00) Her (120.00) 24 = 011 (1,90600) CamScanne X4= 9000 Scanned with

Subsikute equation © 23+24=15 13+1,19,000 = 6,10,000 Hu: 1,19,000 25 = 5,10,000 » 23= 5,10,000 – 1,19,000 L x3 = 3,91,000 X3 valuce subeributing equation ② X2+23=21 22+394.000 = 1 txitx2=-391000 → Addling the equations +42 = 6,80,000 -Mita2 = -391,000 2x2 = 289000 22 = 289000 :: X2 = 1,44500 Scanned with CamScanner

Equation © 22443=X1 © 1,444500 + 391,000 = 1 :: X1 = 1836,000 $18,36,000 $1,44,500 $ 3,91,000 $ 1,19,000 | $ 5,10,000 annual return is X5 > Poojected Z=00.881+0.1272+0.1423 +0.13847010945 Z= 0.08(18.360o) +0.18 (1,44,500) +0.143,9,000) + 0.13(1,19,00) +00915 110.600) Z= 1,46880+17,340 +54,740 +15,470745.900 Z = 2,80,330 :: Pooject annual return = $ 27.80,330 Scanned with CamScanner