Question

Question 7. The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown. Constraint Audience per advertisement Cost per advertisement Maximum media usage Television 100,000 $2000 10 Radio 18,000 $300 Online 40,000 $600 10 20 a. To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. If the promotional budget is limited to $18,200, how many commercial messages should be run on each medium to maximize total audience contact? What is the allocation of the budget among the three media, and what is the total audience reached? For solution, use Excel Solver and provide the screenshots of results from Excel. b. By how much would audience contact increase if an extra $100 were allocated to the promotional budget? Let T= number of television spot advertisements R=number of radio advertisements O= number of online advertisements

Answer 1

a.

Objective Function Value =       1052000.000

      Variable             Value             Reduced Costs  

    --------------        ---------------      ------------------

          T                       4.000                  0.000

          R                    14.000                  0.000

          N                    10.000                  0.000

     Constraint        Slack/Surplus            Dual Prices   

      --------------         ---------------              ------------------

          1                        0.000                           51.304

          2                        6.000                             0.000

          3                        6.000                             0.000

          4                        0.000                    11826.087

          5                        0.000                       5217.391

          6                        1.200                             0.000

OBJECTIVE COEFFICIENT RANGES

   Variable       Lower Limit          Current Value    Upper Limit

------------       ---------------          ---------------              ---------------

       T             -18000.000               100000.000           120000.000

       R              15000.000                 18000.000    No Upper Limit

       N              28173.913                 40000.000    No Upper Limit

RIGHT HAND SIDE RANGES

  Constraint    Lower Limit       Current Value        Upper Limit

   ------------      -------------------    --------------------              ---------------

       1                  14750.000                18200.000                31999.996

       2                          4.000                      10.000       No Upper Limit

       3                        14.000                      20.000       No Upper Limit

       4                          0.000                      10.000                      12.339

       5                         -8.050                        0.000                        2.936

       6         No Lower Limit                        0.000                        1.200

b.         The dual price for the budget constraint is 51.30.  Thus, a $100 increase in budget should provide an increase in audience coverage of approximately 5,130. The right-hand-side range for the budget constraint will show this interpretation is correct.