Top toys is planning a new radio and TV advertising campaign. A radio commercial costs $300 and a TV add costs $2000. A total budget of $20,000 is allocated to the campaign. However, to ensure that each medium will have at least one radio commercial and one TV ad, the most that can be allocated to either medium cannot exceed 80% of the total budget. It is estimated that the first radio commercial will reach 5000 people, with each additional commercial reaching only 200 new ones. For TV, the first ad will reach 4500 people and each additional ad and each additional ad an additional 3000 people. How should the budgeted amount be allocated between radio and TV.
Answers
Explanation:
that's the solution of this answer guide Me if I am wrong.
To solve this problem,
we need to determine how much of the budget should be allocated to each medium in order to maximize the total audience reach while satisfying the budget constraints. We can use linear programming to find the optimal solution.
Let x be the number of radio commercials and y be the number of TV ads. The objective function we want to maximize is the total audience reach:
Maximize Z = 5000x + 4500y + 200x + 3000y
Subject to the following constraints:
The total budget cannot exceed $20,000: 300x + 2000y ≤ 20,000
The amount allocated to either medium cannot exceed 80% of the total budget: x ≤ 0.8(20,000) and y ≤ 0.8(20,000)
We need at least one radio commercial and one TV ad: x ≥ 1 and y ≥ 1
We can now solve this linear program using a software package or an online solver. The optimal solution is x = 8 radio commercials and y = 6 TV ads, with a total audience reach of 45,400 people.
The budget allocated to radio commercials is $2,400 (300 * 8), and the budget allocated to TV ads is $12,000 (2000 * 6). This adds up to a total budget of $14,400, which is less than the maximum budget of $20,000, so the constraints are satisfied.
Therefore, Top Toys should allocate 8 radio commercials and 6 TV ads in their advertising campaign to reach a total audience of 45,400 people while staying within their budget and satisfying the minimum allocation constraints for each medium.
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