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# LP Part II - Linear Programming(LP Models Part 2 LP...

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1 1 Linear Programming (LP) Models: Part 2 LP Modeling Applications with Computer Analysis in Excel Various applications (with Excel files on selected problems): 1. Media selection ( ) 2. Manufacturing ( ) 3. Employee scheduling ( ) 4. Financial investment ( ) 5. Transportation ( ) Reference : Text Chapter 8 Appendix (more LP examples) : A. Marketing research B. Ingredient mix and blending

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2 Learning Objectives 1. Model a variety of linear programming (LP) problems in major business application areas: manufacturing, labor scheduling, finance, transportation, marketing, blending, and multi-period planning . 2. Set up and solve LP problems using Excel’s Solver.
3 Marketing Applications Media Selection  - An organization has budgeted up to \$8,000 per week for local advertising. Money is to be allocated among four promotional media: TV spots, Newspaper ads, and Two types of radio advertisements. Marketing goal - reach out to the largest possible high-potential audience through various media .

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4 Media Selection Data Contract arrangements require at least five radio spots be selected each week. Management insists no more than \$1,800 be spent on radio advertising each week. TV spot (1 minute) 5,000 800 12 Daily newspaper (full-page ad) 8,500 925 5 Radio spot (30 seconds, prime time) 2,400 290 25 Radio spot (1 minute, afternoon) 2,800 380 20
5 LP Formulation for Media Selection Objective: Maximize audience coverage = 5000 X 1 + 8500 X 2 + 2400 X 3 +2800 X 4 Decision variables X 1 = number of 1-minute TV spots selected each week. X 2 = number of full-page daily newspaper ads selected each week. X 3 = number of 30-second prime-time radio spots selected each week. X 4 = number of 1-minute afternoon radio spots selected each week. [More than 2 variables cannot use graphical solution]

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6 LP Formulation for Media Selection Objective: Maximize audience coverage = 5000 X 1 + 8500 X 2 + 2400 X 3 +2800 X 4 subject to: X 1 12 (max TV spots / week) X 2 5 (max newspaper ads / week) X 3 25 (max 30-sec. radio / week) X 4 20 (max 1-min. radio / week) 800 X 1 + 925 X 2 + 290 X 3 + 380 X 4 8000 (weekly advertising budget) X 3 + X 4 5 (min radio spots / week) 290 X 3 + 380 X 4 1800 (max radio expense) X 1 , X 2 , X 3 , X 4 0
7 Optimal Solution On solving the problem by Excel Solver (or other LP package), the optimal media selection is: X 1 = 1.97 TV spots; X 2 = 5.00 newspaper ads; X 3 = 6.21 30-second prime time radio spots; X 4 = 0.00 1-minute afternoon radio spots. This produces an audience exposure of 67,240 contacts.

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8 Manufacturing Applications Product-Mix Problem A nationally known menswear manufacturer produces four varieties of neckties: all-silk tie. all-polyester tie. two different polyester and cotton blends (Blend 1: 50% polyester and 50% cotton; Blend 2: 30 % polyester and 70% cotton)
9 Manufacturing Applications Has fixed contracts with major department stores with the following contract demand for products: All silk All polyester Ploy-cotton blend 1 Ploy-cotton blend 2 6.70 3.55 4.31 4.81 6,000 10,000 13,000 6,000 7,000 14,000 16,000 8,500 0.125 0.08 0.10 0.10 100% silk 100% polyester 50% poly-50% cotton 30% poly-70% cotton

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10 Manufacturing Applications
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