In: Math
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 | Television | Radio | Online |
---|---|---|---|
Audience per advertisement | 100000 | 18000 | 40000 |
Cost per advertisement | $1400 | $300 | $600 |
Maximum media usage | 10 | 20 | 10 |
To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized.
Let | T = number of television spot advertisements |
R = number of radio advertisements | |
O = number of online advertisements |
Budget ($) | |
---|---|
T = | |
R = | |
O = | |
Total Budget = $ |
SOLUTION:
Let
T = number of television spot advertisements
R = number of radio advertisements
O/N = number of Online
Objective function:
Objective function is to maximize the audience reach
Z = max 100000T + 18000R + 40000N
Constraints:
1400T + 300R + 600N <= 16400 (Budget)
T<=10 (Max TV usage)
R<= 20(Max Radio usage)
N<= 10 (Max Online usage)
R<= 0.5*(R + T+N) or -0.5T +0.5 R – 0.5N <= 0 (number of online advertisements)
T>=0.1(T+R+N) or 0.9T – 0.1R – 0.1N >= 0 (television should account for at least 10% of the total number of advertisements)
T,R,N >= 0 (Non negativity constraint)
10 | 0 | 4 | ||
100000 | 18000 | 40000 | =SUMPRODUCT(A$1:C$1,A2:C2) | |
1400 | 300 | 600 | =SUMPRODUCT(A$1:C$1,A3:C3) | 16400 |
1 | 0 | 0 | =SUMPRODUCT(A$1:C$1,A4:C4) | 10 |
0 | 1 | 0 | =SUMPRODUCT(A$1:C$1,A5:C5) | 20 |
0 | 0 | 1 | =SUMPRODUCT(A$1:C$1,A6:C6) | 10 |
-0.5 | 0.5 | -0.5 | =SUMPRODUCT(A$1:C$1,A7:C7) | 0 |
0.9 | -0.1 | -0.1 | =SUMPRODUCT(A$1:C$1,A8:C8) | 0 |
T = 10
R = 0
N /O = 4
Total budget = 16400
b)
Increase in audience =
1166666.667 - 1160000=6667 |