Lingo 做线性规划 - Marketing Applications

Reference: <An Introduction to Management Science Quantitative Approaches to Decision Making, Revised 13th Edition>

Marketing Application 1: Relax-and-Enjoy provided BP&J with an advertising budget of $30,000 for the first month’s campaign. In addition, Relax-and-Enjoy imposed the following restrictions on how BP&J may allocate these funds: At least 10 television commercials must be used, at least 50,000 potential customers must be reached, and no more than $18,000 may be spent on television advertisements. What advertising media selection plan should be recommended?

A1:Build Model as below

Decision variables:

DTV = number of times daytime TV is used
ETV = number of times evening TV is used
DN = number of times daily newspaper is used
SN = number of times Sunday newspaper is used
R = number of times radio is used

R1:Report

Marketing Application 2:Market Survey, Inc. (MSI), specializes in evaluating consumer reaction to new products, services, and advertising campaigns. A client firm requested MSI’s assistance in ascertaining consumer reaction to a recently marketed household product. During meetings with the client, MSI agreed to conduct door-to-door personal interviews to obtain responses from households with children and households without children. In addition, MSI agreed to conduct both day and evening interviews. Specifically, the client’s contract called for MSI to conduct 1000 interviews under the following quota guidelines.
1. Interview at least 400 households with children.
2. Interview at least 400 households without children.
3. The total number of households interviewed during the evening must be at least as great as the number of households interviewed during the day.
4. At least 40% of the interviews for households with children must be conducted during the evening.
5. At least 60% of the interviews for households without children must be conducted during the evening.
Because the interviews for households with children take additional interviewer time and because evening interviewers are paid more than daytime interviewers, the cost varies with the type of interview. Based on previous research studies, estimates of the interview costs are as follows:

What is the household, time-of-day interview plan that will satisfy the contract requirementsat a minimum total interviewing cost?

A1: Build Model as below

DC = the number of daytime interviews of households with children
EC = the number of evening interviews of households with children
DNC = the number of daytime interviews of households without children
ENC = the number of evening interviews of households without children