Cho hệ bất phương trình \(\left\{ \begin{array}{l}0 \le y \le 4\\x \ge 0\\x - y - 1 \le 0\\x + 2y - 10 \le 0\end{array} \right..\) Gọi điểm có toạ độ (x; y) thuộc miền nghiệm của hệ bất phương trình sao cho F(x; y) = x + 2y đạt giá trị lớn nhất. Số điểm thoả mãn là:
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
- Vẽ miền nghiệm của hệ bất phương trình đã cho.
- Xác định các đỉnh của miền nghiệm.
- Tính giá trị của biểu thức $F(x; y) = x + 2y$ tại các đỉnh này.
- Tìm giá trị lớn nhất của $F(x; y)$.
- Xác định số điểm mà tại đó $F(x; y)$ đạt giá trị lớn nhất.
Ta có:
$F(0, 0) = 0 + 2(0) = 0$
$F(1, 0) = 1 + 2(0) = 1$
$F(2, 1) = 2 + 2(1) = 4$
$F(2, 4) = 2 + 2(4) = 10$
$F(0, 4) = 0 + 2(4) = 8$
Vậy, giá trị lớn nhất của $F(x; y)$ là 10, đạt được tại điểm D(2, 4). Do đó, chỉ có 1 điểm thỏa mãn yêu cầu đề bài.
Câu hỏi liên quan
Nguồn năng lượng được sử dụng trong quá trình hóa tổng hợp có nguồn gốc từ đâu?
Anh M mới đăng kí sử dụng 1 loại thẻ mà được chi tiêu, mua sắm thoải mái mặc dù trong thẻ không hề có tiền. Tuy nhiên trong một khoảng thời hạn nhất định nếu anh M không hoàn trả số tiền đã chi tiêu thì anh phải trả một mức lãi theo quy định. Trong trường hợp này, anh M đang sử dụng loại thẻ nào sau đây?
CHỦ ĐỀ 1
(Tham khảo bài văn của chủ đề trong đường link dưới đây ở trang 33)
https://tvsthpt.dlib.vn/app/doc-sach-ebook/d0a01a0e4114
Và trả lời câu hỏi sau:
Trong thí nghiệm 2, nếu sử dụng ánh sáng trắng chiếu vào lăng kính không khí, khi ánh sáng lần lượt khúc xạ qua hai mặt bên và ló ra khỏi lăng kính, nhận định nào sau đây đúng:
Kí hiệu phân lớp nào sau đây là sai?
Cơ sở để quy định tên gọi, trình tự ban hành của văn bản pháp luật là gì?
Cơ năng là một đại lượng
Read the following passage about Traveling and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions from 23 to 30.
Traveling and exploring new places is an exciting way to experience different cultures and expand one’s horizons. Whether it’s a short trip to a neighbouring town or a long journey to a foreign country, stepping out into the world offers numerous benefits. It allows individuals to gain new perspectives, meet diverse people, and create lasting memories. Additionally, traveling can enhance personal growth and provide a sense of adventure and fulfillment.
One of the key advantages of traveling is the opportunity to learn about different cultures. By immersing oneself in a new environment, travellers can gain a deeper understanding of local customs, traditions, and lifestyles. This cultural exchange fosters mutual respect and appreciation among people from different backgrounds. Moreover, experiencing different cultures can challenge preconceptions and broaden one’s worldview.
Traveling also promotes personal development. Facing unfamiliar situations and overcoming challenges can boost confidence and adaptability. Travelers often find themselves navigating new cities, trying unfamiliar foods, and communicating in foreign languages. These experiences can enhance problem-solving skills and resilience. Furthermore, the sense of accomplishment from successfully managing a trip can lead to increased self-esteem and a greater sense of independence.
Another benefit of traveling is the chance to disconnect from the routine of everyday life. Exploring new places provides a break from the usual responsibilities and stresses. This can be refreshing and rejuvenating, allowing individuals to return home with a renewed sense of energy and perspective. Travel can also foster creativity by exposing individuals to new sights, sounds, and ideas.
Despite its benefits, traveling can also present challenges. Planning a trip requires time and effort, and unexpected situations can arise. However, these challenges can be viewed as opportunities for growth and learning. With careful planning and a positive mindset, the rewards of traveling far outweigh the difficulties.
In which paragraph does the writer mention the role of cultural exchange in fostering mutual respect?
Ứng dụng công nghệ nano là hình nào sau đây?
Read the following passage about Champions of the Overlooked and mark the letter A, B, C or D on your answer sheet to indicate the option that best fits each of the numbered blanks from 18 to 22.
In every community, there are special people who help those who cannot speak for themselves. These champions work tirelessly to bring attention to forgotten issues and overlooked individuals. They believe that every person deserves dignity and respect, regardless of their circumstances. Animal rights activists are dedicated individuals (18)_________. Many homeless people are ignored by society, but they deserve our attention and support. Children with disabilities often face barriers to education; however, dedicated teachers create inclusive classrooms for all students. The elderly share their wisdom and experience while needing our care and respect. If more resources were provided, (19)_________. Environmental defenders protect natural habitats and speak for future generations who will inherit our planet. They monitor pollution levels, plant trees, and educate communities about sustainability. These champions often work without recognition, (20)_________.
Volunteers at animal shelters provide food, medical care, and love to abandoned pets. (21)_________. Many of these helpers also advocate for stronger animal protection laws and better education about responsible pet ownership. Their dedication shows us how much impact one person can have on many lives. (22)_________. Their work reminds us that true humanity means caring for all living beings, especially those who cannot advocate for themselves. By supporting these champions, we too can help build a more compassionate and inclusive society where everyone is valued and heard.
Phát biểu nào sau đây là SAI về phần mềm nguồn mở?
Xét hai nguồn sóng kết hợp tạo ra hiện tượng giao thoa trên mặt nước. Cho biết tốc độ truyền sóng là 25 cm/s và tần số sóng là 10 Hz. Tại điểm cách hai nguồn các khoảng bằng bao nhiêu thì sóng có biên độ cực đại?
Vì sao nói Hiến pháp là luật cơ bản của nhà nước có hiệu lực pháp lí cao nhất?
Liên hợp quốc xác định rõ một trong các mục tiêu của tổ chức là thúc đẩy quan hệ hữu nghị giữa các dân tộc trên cơ sở:
Millions of people are using cellphones today. In many places, it is actually considered unusual not to use one. In many countries, cellphones are very popular with young people. They find that the phones are more than a means of communication - having a mobile phone shows that they are cool and connected.
The explosion in mobile phone use around the world has made some health professionals worrieSome doctors are concerned that in the future many people may suffer health problems from the use of mobile phones. In England, there has been a serious debate about this issue. Mobile phone companies are worried about the negative publicity of such ideas. They say that there is no proof that mobile phones are bad for your health.
On the other hand, medical studies have shown changes in the brain cells of some people who use mobile phones. Signs of change in the tissues of the brain and head can be detected with modern scanning equipment. In one case, a traveling salesman had to retire at young age because of serious memory loss. He couldn't remember even simple tasks. He would often forget the name of his own son. This man used to talk on his mobile phone for about six hours a day, every day of his working week, for a couple of years. His family doctor blamed his mobile phone use, but his employer's doctor didn't agree.
What is it that makes mobile phones potentially harmful? The answer is radiation. High-tech machines can detect very small amounts of radiation from mobile phones. Mobile phone companies agree that there is some radiation, but they say the amount is too small to worry about.
As the discussion about their safety continues, it appears that it's best to use mobile phones less often. Use your regular phone if you want to talk for a long time. Use your mobile phone only when you really need it. Mobile phones can be very useful and convenient, especially in emergencies. In the future, mobile phones may have a warning label that says they are bad for your health. So for now, it's wise not to use your mobile phone too often.
Which of the following does the author probably support?
Quốc hội thực hiện có chức năng là gì?
Công trình kiến trúc phòng thủ nào sau đây được xây dựng bởi nhiều triều đại phong kiến Trung Quốc?
Thị trường bao gồm những nhân tố cơ bản nào?
Ý nghĩa của kí hiệu dưới đây là gì?
If he ________ hard today, can he have a holiday tomorrow?
Với tần số hoán vị gen là 20%; cá thể có kiểu gen AB/ab cho tỉ lệ các loại giao tử là?