1. BA 452 Lesson A.8 Marketing and Finance Applications 1 1ReadingsReadings Chapter 4 Linear Programming Applications in Marketing, Finance, and Operations Management

2. BA 452 Lesson A.8 Marketing and Finance Applications 2 2OverviewOverview

3. 3 3Overview Media Selection Problems help marketing managers allocate a fixed advertising budget to various advertising media. The objective is to maximize reach, frequency, and quality of exposure. Marketing Research Problems help marketing managers learn about consumer characteristics and preferences, by surveying sufficiently many people at minimum cost. Portfolio Selection Problems with Dynamic Constraints help select specific investments (stocks, bonds, …) over time to either maximize expected return or minimize risk.

4. BA 452 Lesson A.8 Marketing and Finance Applications 4 4 Tool Summary n One possible way to solve a program where some variables are restricted to be integers (like the number of ads in Example 1): Do not restrict the variables to be integers, and maybe the variables at an optimum will be integers. Warning: This does not always work: without integer restrictions, some variables at an optimum may not be integers --- even if all coefficients in the linear program are integers (like in an Example in Lesson I-3). Warning: This does not always work: without integer restrictions, some variables at an optimum may not be integers --- even if all coefficients in the linear program are integers (like in an Example in Lesson I-3). n Use compound variables: First Example: EFR = number of evening ads on Friday First Example: EFR = number of evening ads on Friday Second Example: G i = amount of new investment in government bonds in month i Second Example: G i = amount of new investment in government bonds in month i Third Example: SO 1 = number of standard wheels made with overtime labor in month 1 Third Example: SO 1 = number of standard wheels made with overtime labor in month 1Overview

5. BA 452 Lesson A.8 Marketing and Finance Applications 5 5 Tool Summary n Use dynamic or recursive constraints: Second Example: Constrain that Month 2's total investment be limited to principle and interest invested locally in Month 1: G 2 + C 2 + L 2 = 1.0075L 1 Second Example: Constrain that Month 2's total investment be limited to principle and interest invested locally in Month 1: G 2 + C 2 + L 2 = 1.0075L 1 n Use inventory variables: Second Example: SI = number of standard wheels held in inventory from month 1 to month 2 Second Example: SI = number of standard wheels held in inventory from month 1 to month 2 Tool Summary

6. BA 452 Lesson A.8 Marketing and Finance Applications 6 6 Media Selection

7. BA 452 Lesson A.8 Marketing and Finance Applications 7 7 Overview Media Selection Problems help marketing managers allocate a fixed advertising budget to various advertising media. Potential media include newspapers, magazines, radio, television, and direct mail. The objective is to maximize reach, frequency, and quality of exposure. Constraints may restrict permissible allocations by company policy, contract requirements, and media availability. Media Selection

8. BA 452 Lesson A.8 Marketing and Finance Applications 8 8 Question: SMM Company recently developed a new instant salad machine, and has $282,000 to spend on advertising. The product is to be initially test marketed in the Dallas area. The money is to be spent on a TV advertising blitz during one weekend (Friday, Saturday, and Sunday) in November. The three options available are: daytime advertising, evening news advertising, and Sunday game-time advertising. A mixture of one-minute TV spots is desired. Media Selection

9. BA 452 Lesson A.8 Marketing and Finance Applications 9 9 Estimated Audience Estimated Audience Ad Type Reached With Each Ad Cost Per Ad Daytime 3,000 $5,000 Evening News 4,000 $7,000 Sunday Game 75,000 $100,000 SMM wants to take out at least one ad of each type (daytime, evening-news, and game-time). Further, there are only two game-time ad spots available. There are ten daytime spots and six evening news spots available daily. SMM wants to have at least 5 ads per day, but spend no more than $50,000 on Friday and no more than $75,000 on Saturday. Media Selection

10. BA 452 Lesson A.8 Marketing and Finance Applications 10 What should be SMM’s objective? Are you making any implicit assumptions? Media Selection

11. BA 452 Lesson A.8 Marketing and Finance Applications 11 Media Selection

12. BA 452 Lesson A.8 Marketing and Finance Applications 12 n Define the decision variables DFR = number of daytime ads on Friday DFR = number of daytime ads on Friday DSA = number of daytime ads on Saturday DSA = number of daytime ads on Saturday DSU = number of daytime ads on Sunday DSU = number of daytime ads on Sunday EFR = number of evening ads on Friday EFR = number of evening ads on Friday ESA = number of evening ads on Saturday ESA = number of evening ads on Saturday ESU = number of evening ads on Sunday ESU = number of evening ads on Sunday GSU = number of game-time ads on Sunday GSU = number of game-time ads on Sunday n Define the objective function Maximize the total audience reached Maximize the total audience reached = Max (audience per ad of each type)x(number of ads used of each type) = Max (audience per ad of each type)x(number of ads used of each type) Max 3000DFR +3000DSA +3000DSU +4000EFR Max 3000DFR +3000DSA +3000DSU +4000EFR +4000ESA +4000ESU +75000GSU +4000ESA +4000ESU +75000GSU Media Selection

13. BA 452 Lesson A.8 Marketing and Finance Applications 13 n Define the constraints to take out at least one ad of each type: (1) DFR + DSA + DSU > 1 (1) DFR + DSA + DSU > 1 (2) EFR + ESA + ESU > 1 (2) EFR + ESA + ESU > 1 (3) GSU > 1 (3) GSU > 1 n Define the constraints of ten daytime spots available: (4) DFR < 10; (5) DSA < 10; (6) DSU < 10 (4) DFR < 10; (5) DSA < 10; (6) DSU < 10 n Define the constraints of six evening news spots available: (7) EFR < 6; (8) ESA < 6; (9) ESU < 6 (7) EFR < 6; (8) ESA < 6; (9) ESU < 6 Media Selection

14. BA 452 Lesson A.8 Marketing and Finance Applications 14 n Define the constraint of only two Sunday game-time ad spots available: (10) GSU < 2 (10) GSU < 2 n Define the constraint of at least 5 ads per day: (11) DFR + EFR > 5; (12) DSA + ESA > 5; (11) DFR + EFR > 5; (12) DSA + ESA > 5; (13) DSU + ESU + GSU > 5 (13) DSU + ESU + GSU > 5 n Define the constraint of spending no more than $50,000 on Friday: (14) 5000DFR + 7000EFR < 50000 (14) 5000DFR + 7000EFR < 50000 n Define the constraint of spending no more than $75,000 on Saturday: (15) 5000DSA + 7000ESA < 75000 (15) 5000DSA + 7000ESA < 75000 n Define the constraint of spending no more than $282,000 in total: (16) 5000DFR + 5000DSA + 5000DSU + 7000EFR (16) 5000DFR + 5000DSA + 5000DSU + 7000EFR + 7000ESA + 7000ESU + 100000GSU7 < 282000 + 7000ESA + 7000ESU + 100000GSU7 < 282000 Define the objective function Define the objective function Media Selection

15. BA 452 Lesson A.8 Marketing and Finance Applications 15 Interpretation: Total new audience reached = 199,000 Interpretation: Total new audience reached = 199,000 Number of daytime ads on Friday = 8 Number of daytime ads on Friday = 8 Number of daytime ads on Saturday = 5 Number of daytime ads on Saturday = 5 Number of daytime ads on Sunday = 2 Number of daytime ads on Sunday = 2 Number of evening ads on Friday = 0 Number of evening ads on Friday = 0 Number of evening ads on Saturday = 0 Number of evening ads on Saturday = 0 Number of evening ads on Sunday = 1 Number of evening ads on Sunday = 1 Number of game-time ads on Sunday = 2 Number of game-time ads on Sunday = 2 Media Selection

16. BA 452 Lesson A.8 Marketing and Finance Applications 16 Marketing Research

17. BA 452 Lesson A.8 Marketing and Finance Applications 17 Overview Marketing Research Problems help marketing managers learn about consumer characteristics and preferences. Marketing research firms design and solve such problems to survey sufficiently many people at minimum cost. Marketing Research

18. BA 452 Lesson A.8 Marketing and Finance Applications 18 Question: C R Market Surveys, Inc. specializes in evaluating consumer reaction to new products and advertising campaigns. A client hired Market Survey Inc. to measure consumer reaction to a recently marketed product. Market Survey Inc. agreed to conduct interviews from households, both with or without children, during either the day or evening. Marketing Research

19. BA 452 Lesson A.8 Marketing and Finance Applications 19 The client’s contract calls for 1000 interviews under the following quotas: 1. Interview at least 400 households with children. 2. Interview at least 400 households without children. 3. Interview at least as many households at night, as during the day. 4. Of the interviews of households with children, at least 40 percent must be during the evening. 5. Of the interviews of households without children, at least 60 percent must be during the evening. Based on previous studies, here are the estimated interview costs: Formulate the Marketing Research Problem for finding the minimum- cost household, time-of-day interview plan satisfying all quotas. Marketing Research HouseholdDayEvening Children$20$25 No Children $18$20

20. BA 452 Lesson A.8 Marketing and Finance Applications 20 Answer: Define decision variables DC = the number of daytime interviews of households with children DN = the number of daytime interviews of households with no children EC = the number of evening interviews of households with children EN = the number of evening interviews of households with no children Marketing Research

21. BA 452 Lesson A.8 Marketing and Finance Applications 21 Given cost per unit, minimize total cost: Min 20DC + 18DN + 25EC + 20EN Marketing Research HouseholdDayEvening Children$20$25 No Children $18$20

22. BA 452 Lesson A.8 Marketing and Finance Applications 22 Formulate Constraints: 1. Interview at least 1000 households: DC + DN + EC + EN > 1000 2. Interview at least 400 households with children: DC + EC > 400 3. Interview at least 400 households without children: DN + EN > 400 4. Interview at least as many households at night, as during the day: EC + EN > DC + DN 5. Of the interviews of households with children, at least 40 percent must be during the evening: EC > 0.40(DC + EC) 6. Of the interviews of households without children, at least 60 percent must be during the evening: EN > 0.60(DN + EN) Marketing Research

23. BA 452 Lesson A.8 Marketing and Finance Applications 23 Portfolio Selection with Dynamic Constraints

24. BA 452 Lesson A.8 Marketing and Finance Applications 24 Overview Portfolio Selection Problems with Dynamic Constraints help financial managers select specific investments (stocks, bonds, …) over time to either maximize expected return or minimize risk. Dynamic Constraints may restrict new investment in one period to equal the return from investments in previous periods. For example, there may be no new investments one month if all investments in previous months have not yet matured. Portfolio Selection with Dynamic Constraints

25. BA 452 Lesson A.8 Marketing and Finance Applications 25 Question: Pepperdine University has $20 million available for investment. It wishes to invest over the next four months in such a way that it will maximize the total interest earned (after all investments mature) as well as have at least $10 million available at the start of the fifth month for a high rise building venture in which it will be participating. For the time being, Pepperdine wishes to invest only in 2-month government bonds (earning 2% over the 2-month period) and 3-month construction loans (earning 6% over the 3-month period). Each of these is available each month for investment. Funds not invested in these two investments are liquid and earn 3/4 of 1% per month when invested locally. How should Pepperdine invest over the next four months if at no time does it wish to have more than $8 million in either government bonds or construction loans? Portfolio Selection with Dynamic Constraints

26. BA 452 Lesson A.8 Marketing and Finance Applications 26 Answer: Define the decision variables G i = amount of new investment in government G i = amount of new investment in government bonds in month i (for i = 1, 2, 3, 4) bonds in month i (for i = 1, 2, 3, 4) C i = amount of new investment in construction C i = amount of new investment in construction loans in month i (for i = 1, 2, 3, 4) loans in month i (for i = 1, 2, 3, 4) L i = amount invested locally in month i (for i = 1, 2, 3, 4) L i = amount invested locally in month i (for i = 1, 2, 3, 4) Portfolio Selection with Dynamic Constraints

27. BA 452 Lesson A.8 Marketing and Finance Applications 27 n Define the objective function Maximize total interest earned after all investments mature: Maximize total interest earned after all investments mature: Max (interest rate on investment) X (amount invested) Max (interest rate on investment) X (amount invested) Max.02G 1 +.02G 2 +.02G 3 +.02G 4 Max.02G 1 +.02G 2 +.02G 3 +.02G 4 +.06C 1 +.06C 2 +.06C 3 +.06C 4 +.06C 1 +.06C 2 +.06C 3 +.06C 4 +.0075L 1 +.0075L 2 +.0075L 3 +.0075L 4 +.0075L 1 +.0075L 2 +.0075L 3 +.0075L 4 Portfolio Selection with Dynamic Constraints

28. BA 452 Lesson A.8 Marketing and Finance Applications 28 n Constrain that Month 1's total investment be $20 million: (1) G 1 + C 1 + L 1 = 20,000,000 (1) G 1 + C 1 + L 1 = 20,000,000 n Constrain that Month 2's total investment be limited to principle and interest invested locally in Month 1: (2) G 2 + C 2 + L 2 = 1.0075L 1, or G 2 + C 2 - 1.0075L 1 + L 2 = 0 (2) G 2 + C 2 + L 2 = 1.0075L 1, or G 2 + C 2 - 1.0075L 1 + L 2 = 0 n Constrain that Month 3's total investment be limited to principle and interest invested in government bonds in Month 1 and locally invested in Month 2: (3) G 3 + C 3 + L 3 = 1.02G 1 + 1.0075L 2, or - 1.02G 1 + G 3 + C 3 - 1.0075L 2 + L 3 = 0 (3) G 3 + C 3 + L 3 = 1.02G 1 + 1.0075L 2, or - 1.02G 1 + G 3 + C 3 - 1.0075L 2 + L 3 = 0 Portfolio Selection with Dynamic Constraints

29. BA 452 Lesson A.8 Marketing and Finance Applications 29 n Constrain that Month 4's total investment be limited to principle and interest invested in construction loans in Month 1, government bonds in Month 2, and locally invested in Month 3: (4) G 4 + C 4 + L 4 = 1.06C 1 + 1.02G 2 + 1.0075L 3, or (4) G 4 + C 4 + L 4 = 1.06C 1 + 1.02G 2 + 1.0075L 3, or - 1.02G 2 + G 4 - 1.06C 1 + C 4 - 1.0075L 3 + L 4 = 0 - 1.02G 2 + G 4 - 1.06C 1 + C 4 - 1.0075L 3 + L 4 = 0 n Constrain that $10 million must be available at start of Month 5: (5) 1.02G 3 + 1.06C 2 + 1.0075L 4 > 10,000,000 (5) 1.02G 3 + 1.06C 2 + 1.0075L 4 > 10,000,000 Portfolio Selection with Dynamic Constraints

30. BA 452 Lesson A.8 Marketing and Finance Applications 30 n Constrain that no more than $8 million be in government bonds at any time: (6) G 1 < 8,000,000; (7) G 1 + G 2 < 8,000,000 (6) G 1 < 8,000,000; (7) G 1 + G 2 < 8,000,000 (8) G 2 + G 3 < 8,000,000; (9) G 3 + G 4 < 8,000,000 (8) G 2 + G 3 < 8,000,000; (9) G 3 + G 4 < 8,000,000 n Constrain that no more than $8 million be in construction loans at any time: (10) C 1 < 8,000,000; (11) C 1 + C 2 < 8,000,000 (10) C 1 < 8,000,000; (11) C 1 + C 2 < 8,000,000 (12) C 1 + C 2 + C 3 < 8,000,000; (13) C 2 + C 3 + C 4 < 8,000,000 (12) C 1 + C 2 + C 3 < 8,000,000; (13) C 2 + C 3 + C 4 < 8,000,000 Portfolio Selection with Dynamic Constraints

31. BA 452 Lesson A.8 Marketing and Finance Applications 31 Interpretation: Total interest earned in the 4-month period = $1,429,213.80. G i = invested in government bonds C i = invested in construction loans L i = invested locally, in month i (for i = 1, 2, 3, 4) Portfolio Selection with Dynamic Constraints

32. BA 452 Lesson A.8 Marketing and Finance Applications 32 BA 452 Quantitative Analysis End of Lesson A.8