Question

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Chapter 04 LP Applications 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 8 12 14 Furniture loans Other secured loans Signature loans Risk-free securities 13 9 The credit union will have $1.2 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 signature loans may not exceed the funds invested in risk-free securities. How should the $1.2 million be allocated to each of the loan/investment alternatives to maximize total annual return? Round your answers to the nearest dollar. Automobile Loans $ 756,000 X

Answer 1

Furnituse loans (x2) Automobile loans (x) Other secured loans (63) Signatux loans (0) Risk-free securities («s.) Maximize p = 0.08x1 + 0.1222 +0.164 X2 + 0-1324 + 0.0935 Subject to the constraints : liy Xit x₂ + x3 + xut as a 1,200,000 as < 1, 200,000 X 30% 360.000 Rss Wis 24 (2,+ x2 + x3 + x4) x 10°%. 0.9.24 - Qu 1261 0-12 0.1 xg! e o iv) Hz + x3 = x x₂ + xzxco x + xy exs xz + xy - xsso vi) to xy X, YO وعلاوہ لهيلا,هجولاہهلاهلا

B c D E A 1 Variables 2 x1 3 x2 4 x3 ооооо 5 x4 6 x5 7 8 Objective 9 10 Maximize 11 12 Constraints 13 0 14 1 0 11 0 1,200,000 360,000 0 15 16 17 N 0 < 0 3 4 5 6 0 0 18 5 n 0 19 Y Y Y Y Y w w w w 0 20 7 0 0 21 8 0 oc 22 9 10 0 0 23 0

B с D O O O O O А 1 Variables 2 x1 3 X2 4 x3 5 X4 6 X5 7 8 Objective 9 10 Maximize 11 12 Constraints 13 =0.08*B2+0.12*B3+0.14*B4+0.13*B5+0.09*B6 14 1 1200000 15 2 < 360000 16 3 =B2+B3+B4+B5+B6 =B6 =0.9*B5-0.1*B2-0.1*B3-0.1*B4 =B3+B4-B2 =B4+B5-B6 0 17 4 <= 0 18 5 0 19 6 =B2 0 20 7 =B3 >= 0 =B4 0 21 8 22 9 23 10 >= 0 =B5 =B6 0 24

Solver Parameters X B с D E F Set Objective: $B$10 А 1 Variables 2 x1 3 X2 4 x3 5 X4 6 X5 0 0 0 To: O Max Min Value Of: 0 0 By Changing Variable Cells: 0 $B$2:$B$6 7 8 Objective 9 Add 0 10 Maximize 11 Change Subject to the Constraints: $B$14 = $D$14 $B$15 <= $D$15 $B$16 <= $D$16 $B$17 <= $D$17 $B$18 <= $D$18 $B$19 >= $D$19 $B$20 >= $D$20 $B$21 >= $D$21 $B$22 >= $D$22 $B$23 >= $D$23 12 Constraints 13 14 1 Delete 0 = 15 2 0 1,200,000 360,000 0 Reset All 3 16 17 0 0 4 0 Load/Save 18 5 0 < 0 Make Unconstrained variables Non-Negative Y Y Y Y Y ll ll ll ll l. 19 6 0 0 Select a Solving Method: Simplex LP Options 7 0 0 20 21 8 0 0 22 9 0 0 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 non-smooth. 23 10 0 0 24

B с D E A 1 Variables 2 x1 3 x2 4 x3 5 x4 6 x5 7 8 Objective 9 10 Maximize $378,000 $102,000 $276,000 $84,000 $360,000 $124,440 12 Constraints 1 1200000 8 Ե Ե Ե Ե Ե Ի Ե Ե E = 2 360000 1,200,000 360,000 0 16 3 0 <= st 0 <= 0 0 0 5 6 >= 0 >= 0 7 8 378000 102000 276000 84000 >= 0 21 22 9 >= 0 23 10 360000 0 24