15. The Investment Club at Bell Labs has solicited and obtained $50,000 from its members. Collectively,...
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15. The Investment Club at Bell Labs has solicited and obtained $50,000 from its members. Collectively, the members have selected the three stocks, two bond funds, and a tax-deferred annuity shown in the following table as possible investments (let Xi-$ invested in option i, i=1, 2, 3, 4, 5, and 6). Formulate and solve a linear program that will maximize the total projected annual return subject to the conditions set forth by the Investment Club members. Decision Variable ● X₁ X2 X3 X4 X5 X6 ● Investment Option Stock-EAL Stock-BRU Stock-TAT Risk High Moderate Low Bonds- long term Bonds-short term Tax-deferred annuity The club members have decided on the following strategies for investment: All $50,000 is to be invested. At least $10,000 is to be invested in the tax-deferred annuity. At least 25% of the funds invested in stocks are to be in the low-risk stock (i.e. TAT). No more than $12,500 of the total investment is to be placed in investments with projected annual returns of less than 10% (i.e. TAT, Short term Bonds, and Tax-deferred annuity) At least as much is to be invested in bonds as stocks. Projected Annual Return 15% 12% 9% 11% 8% 6% 5 Req.1 6 Req 2 7 Req 3 8 9 1 PE-LP 2 3 Parameters 4 Req 4 Req 5 10 Return/unit 11 12 Decision Variable 13 A 14 Quantity 15 16 Model Outputs 17 18 Req.1 19 Req.2 20 Req.3 21 Req.4 22 Req.5 23 Tot Retum: X1 1 -0.25 -1 0.15 X1 0 Left-Hand Side =SUMPRODUCT(B5:1 =SUMPRODUCT(B6:1 =SUMPRODUCT(B7:1 =SUMPRODUCT(B8:¹ =SUMPRODUCT(89: X2 1 -0.25 -1 0.12 X2 0 X3 1 0.75 1 -1 0.09 X3 0 D 1 0.11 PX X4 1 X4 0 E X5 1 1 : 1 0.08 X5 0 F X6 1 1 1 0.06 X6 0 G >= <= >= H Limits/Req. 50000 10000 0 12500 0 15. One typo can be found in (a) cell B7, (b) cell B9, (c) cell B18, (d) cell B21, (e) cell D10, (f) cell 17, (g) cell B23, (h) none of the above. 15. The Investment Club at Bell Labs has solicited and obtained $50,000 from its members. Collectively, the members have selected the three stocks, two bond funds, and a tax-deferred annuity shown in the following table as possible investments (let Xi-$ invested in option i, i=1, 2, 3, 4, 5, and 6). Formulate and solve a linear program that will maximize the total projected annual return subject to the conditions set forth by the Investment Club members. Decision Variable ● X₁ X2 X3 X4 X5 X6 ● Investment Option Stock-EAL Stock-BRU Stock-TAT Risk High Moderate Low Bonds- long term Bonds-short term Tax-deferred annuity The club members have decided on the following strategies for investment: All $50,000 is to be invested. At least $10,000 is to be invested in the tax-deferred annuity. At least 25% of the funds invested in stocks are to be in the low-risk stock (i.e. TAT). No more than $12,500 of the total investment is to be placed in investments with projected annual returns of less than 10% (i.e. TAT, Short term Bonds, and Tax-deferred annuity) At least as much is to be invested in bonds as stocks. Projected Annual Return 15% 12% 9% 11% 8% 6% 5 Req.1 6 Req 2 7 Req 3 8 9 1 PE-LP 2 3 Parameters 4 Req 4 Req 5 10 Return/unit 11 12 Decision Variable 13 A 14 Quantity 15 16 Model Outputs 17 18 Req.1 19 Req.2 20 Req.3 21 Req.4 22 Req.5 23 Tot Retum: X1 1 -0.25 -1 0.15 X1 0 Left-Hand Side =SUMPRODUCT(B5:1 =SUMPRODUCT(B6:1 =SUMPRODUCT(B7:1 =SUMPRODUCT(B8:¹ =SUMPRODUCT(89: X2 1 -0.25 -1 0.12 X2 0 X3 1 0.75 1 -1 0.09 X3 0 D 1 0.11 PX X4 1 X4 0 E X5 1 1 : 1 0.08 X5 0 F X6 1 1 1 0.06 X6 0 G >= <= >= H Limits/Req. 50000 10000 0 12500 0 15. One typo can be found in (a) cell B7, (b) cell B9, (c) cell B18, (d) cell B21, (e) cell D10, (f) cell 17, (g) cell B23, (h) none of the above.
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Managerial Decision Modeling with Spreadsheets
ISBN: 978-0136115830
3rd edition
Authors: Nagraj Balakrishnan, Barry Render, Jr. Ralph M. Stair
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