Mixed Problems Five Categories of Linear Programming Problems
Mixed Problems
Five Categories of Linear Programming Problems • Resource Allocation • Cost Benefit Trade Off • Mixed Problems • Transportation • Assignment
Mixed Problems • Use the constraints of both resource allocation and cost benefit trade off. • They also use a fixed requirement. • <= • >= • =
Continuing the Super Grain Case Study • David and Claire conclude that the spreadsheet model needs to be expanded to incorporate some additional considerations. • In particular, they feel that two audiences should be targeted — young children and parents of young children. • Two new goals • The advertising should be seen by at least five million young children. • The advertising should be seen by at least five million parents of young children. • Furthermore, exactly $1, 490, 000 should be allocated for centsoff coupons. 3 -4
Benefit and Fixed-Requirement Data Number Reached in Target Category (millions) Each TV Commercial Each Magazine Ad Each Sunday Ad Minimum Acceptable Level Young children 1. 2 0. 1 0 5 Parents of young children 0. 5 0. 2 5 Contribution Toward Required Amount Coupon redemption Each TV Commercial Each Magazine Ad Each Sunday Ad Required Amount 0 $40, 000 $120, 000 $1, 490, 000 3 -5
Spreadsheet Formulation 3 -6
Algebraic Formulation Let TV = Number of commercials for separate spots on television M = Number of advertisements in magazines. SS = Number of advertisements in Sunday supplements. Maximize Exposure = 1, 300 TV + 600 M + 500 SS subject to Ad Spending: 300 TV + 150 M + 100 SS ≤ 4, 000 ($thousand) Planning Cost: 90 TV + 30 M + 30 SS ≤ 1, 000 ($thousand) Number of TV Spots: TV ≤ 5 Young children: 1. 2 TV + 0. 1 M ≥ 5 (millions) Parents: 0. 5 TV + 0. 2 M + 0. 2 SS ≥ 5 (millions) Coupons: 40 M + 120 SS = 1, 490 ($thousand) and TV ≥ 0, M ≥ 0, SS ≥ 0. 3 -7
Template for Mixed Problems 3 -8
- Slides: 8