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Tonya Manager is interested in expanding her firm and has determined three areas in which she might invest additional funds: (1) product research and development, (2) man- ufacturing operations improvements, and (3) advertising and sales promotion. Tonya has $500,000 available for investment in the firm. She can invest in its advertising and sales promotion program every year, and each dollar invested in this manner is expected to yield a return of the amount invested plus 20% yearly. She can invest in manufacturing operations improvements every 2 years, with an expected return of the investment plus 30% (at the end of each 2-year period). An investment in product research and develop- ment would be for a 3-year period, with an expected return of the investment plus 50% (at the end of the 3-vear period)

Tonya Manager is interested in expanding her firm and has determined three areas in which she might invest additional funds: (1) product research and development, (2) man- ufacturing operations improvements, and (3) advertising and sales promotion. Tonya has $500,000 available for investment in the firm. She can invest in its advertising and sales promotion program every year, and each dollar invested in this manner is expected to yield a return of the amount invested plus 20% yearly. She can invest in manufacturing operations improvements every 2 years, with an expected return of the investment plus 30% (at the end of each 2-year period). An investment in product research and develop- ment would be for a 3-year period, with an expected return of the investment plus 50% (at the end of the 3-vear period)

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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3. Tonya Manager is interested in expanding her firm and has determined three areas in which she might invest additional funds: (1) product research and development, (2) man- ufacturing operations improvements, and (3) advertising and sales promotion. Tonya has $500,000 available for investment in the firm. She can invest in its advertising and sales promotion program every year, and each dollar invested in this manner is expected to yield a return of the amount invested plus 20% yearly. She can invest in manufacturing operations improvements every 2 years, with an expected return of the investment plus 30% (at the end of each 2-year period). An investment in product research and develop- ment would be for a 3-year period, with an expected return of the investment plus 50% (at the end of the 3-year period). To diversify the total initial investment, Tonya wishes to include the requirement that at the beginning of the first year at least $30,000 must be invested in the advertising and sales promotion program, at least $40,000 in manufacturing operations improvements, and at least $50,000 in product research and development initially. All $500,000 must be invested at the beginning of the first year. You may assume all returns in year t can be reinvested in year t + 1. (a) Formulate a linear program to determine how much should be invested in each of the three alternatives, during each year of a 4-year period, to maximize the total value of the investments at the end of the 4-year period.
Transcribed Image Text:3. Tonya Manager is interested in expanding her firm and has determined three areas in which she might invest additional funds: (1) product research and development, (2) man- ufacturing operations improvements, and (3) advertising and sales promotion. Tonya has $500,000 available for investment in the firm. She can invest in its advertising and sales promotion program every year, and each dollar invested in this manner is expected to yield a return of the amount invested plus 20% yearly. She can invest in manufacturing operations improvements every 2 years, with an expected return of the investment plus 30% (at the end of each 2-year period). An investment in product research and develop- ment would be for a 3-year period, with an expected return of the investment plus 50% (at the end of the 3-year period). To diversify the total initial investment, Tonya wishes to include the requirement that at the beginning of the first year at least $30,000 must be invested in the advertising and sales promotion program, at least $40,000 in manufacturing operations improvements, and at least $50,000 in product research and development initially. All $500,000 must be invested at the beginning of the first year. You may assume all returns in year t can be reinvested in year t + 1. (a) Formulate a linear program to determine how much should be invested in each of the three alternatives, during each year of a 4-year period, to maximize the total value of the investments at the end of the 4-year period.
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