due on 12/14

profilesuzies_119
lineprogramming.xlsx
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Intro

Linear Programming
3 elements
(1) Decision Variables - Solutions
(2) Objective - Maximization or Minimization
(3) Constraints - Restrictions

Media

X1 (Day TV) X2 (Evening TV) X3 (Daily Papers) X4 (Sunday Papers) X5 (Radio) RHS 3 kinds of Variables LINEAR PROGRAMMING MODEL
SOLUTIONS 10 0 25 2 30 (A) Marketing Plan Slack Variables unused resource
10 Day TV Ads Surplus Variables excess production (1) Decision Variables
OBJECTIVES 65 90 40 60 20 2370 0 Evening TV Shadow Price value of the objective
25 Daily Papers X1 Number of Daytime TV Ads
2 Sunday Papers X2 Number of Nightime TV Ads
30 Radio ex: class has 50 seats X3 Number of Daily Papers Ads
but 4 empty seat in class slack X4 Number of Sunday Papers Ads
Obtimal results of objective 2370 Exposure Units X5 Number of Radio Ads
CONSTRAINTS 1 10 15
1 0 10 7:00 AM class (2) Objectives
1 25 25 (B) Is the entire advertising budget all utilized? 8:15 AM
1 2 4 class ends at 8:20 AM Maximize = 65X1 + 90X2 + 40X3 + 60X4 + 20X5 Expecting Exposure Units
1 30 30 The entire ads budget of $30,000 is all utilized. (no mooney left = spend it all) you get 5 more minute FREE of tuition surplus A.C. Nielsen - Rating Company
1500 3000 400 1000 100 30000 30000
1 1 10 10 (3) Constraints
1500 3000 15000 18000 ( C) Does the plan satisfy the TV requirements? Right Hand side (RHS)
1000 2000 1500 2500 300 61500 50000 X1 ≤ 15 (Daytime TV Ads)
The client's requirement of "at least 10 TV ads" is satisfied. X2 ≤ 10 (Evening TV Ads)
10 Day TV Ads X3 ≤ 25 (Daily Papers Ads)
X4 ≤ 4 (Sunday Papers Ads)
X5 ≤ 30 (Radio Ads)
always start CONSTRAINTS from 10 (D) Is the TV budget all used up? Any leftover money? $1,500X1 $3,000X2 $400X3 $1,000X4 $100X5 ≤ $30,000 (Ad Budget)
10 Tv
X1 X2 ≥ 10 (TV Ads)
The TV budget of $18,000 is not all used up. $1,500X1 $3,000X2 ≤ $18,000 (TV Budget)
Leftover money 3000 slack variable 1,000X1 2,000X2 1,500X3 2,500X4 300X5 ≥ 50,000 (Families)
Microsoft Excel 16.0 Sensitivity Report ( E) How many potential families are reached?
Worksheet: [line programming.xlsx]Media
Report Created: 11/17/2021 11:08:24 PM 61500 families are reached
What is the difference from our RHS?
Variable Cells what kind of variables would that be?
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease difference 11500 families surplus variable
$B$2 SOLUTIONS X1 (Day TV) 10 0 65 25 65
$C$2 SOLUTIONS X2 (Evening TV) 0 -65 90 65 1E+30
$D$2 SOLUTIONS X3 (Daily Papers) 25 0 40 1E+30 16 (F) if extra funds are available, which media would you invest in?
$E$2 SOLUTIONS X4 (Sunday Papers) 2 0 60 40 16.6666666667 state your ranking
$F$2 SOLUTIONS X5 (Radio) 30 0 20 1E+30 14
Ranking (from higher exposure units - least)
Constraints best (1) Daily paper (shadow price of 16 exposure units)
Final Shadow Constraint Allowable Allowable (2) Radio (shadow price of 14 exposure units)
Cell Name Value Price R.H. Side Increase Decrease
$H$10 CONSTRAINTS 10 0 15 1E+30 5 slack variable
$H$11 0 0 10 1E+30 10
$H$12 25 16 25 5 5 daily paper has a shadow price of 16 exposure units
$H$13 2 0 4 1E+30 2
$H$14 30 14 30 20 20 radio has a shadow price of 14 exposure units
$H$15 30000 0.06 30000 2000 2000
$H$16 10 -25 10 1.3333333333 1.3333333333
$H$17 15000 0 18000 1E+30 3000
$H$18 61500 0 50000 11500 1E+30