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The image you uploaded contains some text in Chinese. Let me first transcribe and translate it so I can assist you in solving the problem or building the required mathematical model.

I'll start by extracting the content.The text in the image contains a problem that seems to focus on creating and solving a mathematical model based on the provided information.

Here is the transcription:

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**问题**: 某地区的甲种疫苗、乙种疫苗可有效预防上呼吸道疾病, 现有部分不完全免疫的小孩, 将安排接种其中一种疫苗, 接种时每个小孩只可选择其中一种疫苗。 甲种和乙种疫苗分别对该病有70%和60%的预防效果。

安排接种时, 要求至少95%的小孩得到有效预防, 假设每个小孩接种疫苗后是否能得到有效预防是独立的事件。

(1) 如何安排接种, 使得需要接种疫苗的小孩人数最少。 请建立数学模型并求解。

(2) 若现有甲种疫苗可供接种的总人数不足, 修改模型并求解。

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### Translation:

**Problem**: In a certain region, Vaccine A and Vaccine B can effectively prevent upper respiratory diseases. A number of partially immunized children will be arranged to receive one of these vaccines, and each child can only choose one vaccine. Vaccine A and Vaccine B have a preventive effect of 70% and 60%, respectively.

When arranging vaccinations, it is required that at least 95% of the children receive effective prevention. Assume that whether each child receives effective prevention after vaccination is an independent event.

(1) How should the vaccinations be arranged to minimize the number of children needing vaccination? Please create a mathematical model and solve it.

(2) If the available Vaccine A is insufficient for all children, modify the model and solve it.

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Learn how to solve a mathematical model for optimizing vaccine distribution to achieve effective prevention in at least 95% of children using Vaccine A and B. This problem covers key concepts in probability and optimization. Suitable for undergraduate students.

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