Question

Кандидат в депутаты за время избирательной компании имеет право на одно бесплатное выступление в газете, а также на платные выступления по радио и телевидению. Выступление в газете увеличивает число сторонников кандидата на 1000 человек; каждое выступление по радио увеличивает количество голосов на 40% и стоит 42 тысячи рублей; каждое выступление по телевидению – на 80% и стоит 47 тысяч рублей. Определите количество и последовательность выступлений в этих средствах массовой информации, при которых кандидат получит наибольшее возможное число голосов, если на всю компанию можно израсходовать не более 112 тысяч рублей

Answer 1

Вначале выступление в газете а затем телевидение и радио или радио и телевидение - будет добавление одинакового количества избирателей .

Answer 2

Introduction

In an electoral campaign, a candidate for deputy has the right to one free speech in a newspaper, as well as paid speeches on radio and television. Each newspaper speech increases the candidate's number of supporters by 1000 people. Each radio speech increases the number of votes by 40% and costs 42,000 rubles. Each television speech increases the number of votes by 80% and costs 47,000 rubles. The task is to determine the number and sequence of speeches in these media that will result in the candidate receiving the maximum possible number of votes, given a budget of no more than 112,000 rubles.

Solution

To determine the optimal number and sequence of speeches, we need to consider the budget constraint and the impact of each type of speech on the number of votes.

Let's analyze the options:

1. Free speech in a newspaper: This speech increases the candidate's number of supporters by 1000 people. Since it is free, it does not affect the budget.

2. Paid speeches on radio: Each radio speech increases the number of votes by 40% and costs 42,000 rubles.

3. Paid speeches on television: Each television speech increases the number of votes by 80% and costs 47,000 rubles.

To maximize the number of votes within the budget constraint, we need to find the optimal combination of these speeches.

Let's consider the possible scenarios:

Scenario 1: Only free speech in a newspaper - Number of newspaper speeches: 1 - Number of radio speeches: 0 - Number of television speeches: 0 - Total cost: 0 rubles - Total increase in votes: 1000 people

Scenario 2: One radio speech - Number of newspaper speeches: 0 - Number of radio speeches: 1 - Number of television speeches: 0 - Total cost: 42,000 rubles - Total increase in votes: 40%

Scenario 3: One television speech - Number of newspaper speeches: 0 - Number of radio speeches: 0 - Number of television speeches: 1 - Total cost: 47,000 rubles - Total increase in votes: 80%

Scenario 4: One radio speech and one television speech - Number of newspaper speeches: 0 - Number of radio speeches: 1 - Number of television speeches: 1 - Total cost: 42,000 + 47,000 = 89,000 rubles - Total increase in votes: 40% + 80%

Based on these scenarios, we can see that the optimal combination is to have one radio speech and one television speech. This will maximize the number of votes while staying within the budget constraint.

Therefore, the candidate should give one radio speech and one television speech to receive the maximum possible number of votes.

Note: The specific order of the speeches (whether the radio speech should come before the television speech or vice versa) is not specified in the question. Therefore, any order that includes one radio speech and one television speech will be considered as a valid solution.

Conclusion

To receive the maximum possible number of votes within a budget of 112,000 rubles, the candidate should give one radio speech and one television speech. The order of these speeches can be determined based on campaign strategy and other factors.