ABC Retail is planning next year’s advertising mix to promote their latest produ
ID: 2780129 • Letter: A
Question
ABC Retail is planning next year’s advertising mix to promote their latest products. Television, newspaper, and online ads are being proposed. The following table shows estimates of audience reach, costs, and individual upper limits on each type of ad. Type of ad Cost per ad Audience reached per ad Upper limit on ads of this type Television $2,000 100,000 10 Online $600 40,000 10 Newspaper $500 15,000 8 The budget for ads is limited to $15,000. To ensure a balanced used of the three media, online ads must not exceed 50% of the total number of ads and television ads must account for at least 10% of the total number of ads. Write the linear programming formulation to help ABC determine the best mix of ads that will maximize the total audience reached.
Explanation / Answer
The linear programming can be formulated as:
Suppose,
No. of televisions ad = X
No. of online ad = Y
No. of newspaper ad = Z
Now,
Budeget:
2000*X + 600*Y + 500*Z <= 15000
Balanced usage:
Y <=(X+Y+Z)/2
Y<= X+Z
X >= (X+Y+Z)*0.1
0.9*X >= Y+Z
Limit
X<=10
Y<= 10
Z< = 8
Max. Audience Reach (F)
Max. F = 100000*X + 40000*Y + 15000*Z
Solving the above equation,
X=3
Y=9
Z=7