Question

Problem 4-01 (Algorithmic)

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 newspaper. Audience estimates, costs, and maximum media usage limitations are as shown:

Constraint	Television	Radio	Newspaper
Audience per advertisement	100000	18000	20000
Cost per advertisement	$2000	$300	$600
Maximum media usage	10	20	10

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.

1. If the promotional budget is limited to $31,100, 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? If required, round your answers to the nearest dollar.
   

   Let	T = number of television spot advertisements
   	R = number of radio advertisements
   	N = number of newspaper advertisements

   	Budget ($)
   T =
   R =
   N =
   	Total Budget = _____$

   
   What is the total audience reached? Round your answer to the nearest whole number.
   
   ________________
   
2. By how much would audience contact increase if an extra $100 were allocated to the promotional budget? Round your answer to the nearest whole number.
   

_________________

Answer 1

Let the number of television ads be x, radio be y and online be z

Objective is to maximize the audience reach

Max Z = 100000x + 18000y + 20000z

Constraints -

y <= 0.50 (x+y+z) ... radio ads less than 50% of total ads

x >= 0.10 (x+y+z) ... tv ads should be atleast 10% of total ads

2000x + 300y + 600z <= 31100 ... total budget available

x <= 10 ... maximum tv ads

y <= 20 ... maximum radio ads

z <= 10 ... maximum online ads

x, y, z >= 0 ... non negativity constraint

Let us solve using excel solver -

Let us initially assume that x, y, z = 1 (blue cells). We need to optimize these to find the maximum reach (green cell)

Run solver to get -

Hence, Number of television ads = 10, radio ads = 19 and newspaper ads = 9

Budget allocation for tv ad = 2000*10 = 20000
Budget allocation for newspaper ad = 300*19 = 5700
Budget allocation for online ad = 600*9 = 5400

Total reach = 1522000

(b) If $100 extra were allocated to the total budget, the constraints would changes as below -

y <= 0.50 (x+y+z) ... radio ads less than 50% of total ads

x >= 0.10 (x+y+z) ... tv ads should be atleast 10% of total ads

2000x + 300y + 600z <= 31200 ... total budget available

x <= 10 ... maximum tv ads

y <= 20 ... maximum radio ads

z <= 10 ... maximum online ads

x, y, z >= 0 ... non negativity constraint

Configure the solver and run the solver -

Run to get -

There would be no change in the audience reach if the budget is increased by $100.

This is because all the other constraints remain same.