Cara menyelesaikan program linear dengan mudah dibahas di artikel ini melalui contoh nyata di kehidupan sehari-hari dan lingkungan sekitar.

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Contoh Soal Program Linear dan Pembahasannya. Daerah penyelesaian dari masalah di atas terlihat pada daerah yang diarsir: R(5,0) Q(1,2) P(0,5) Dengan menguji titik-titik sudut daerah penyelesaian diperoleh. Thx atas soal dan pembahasan nya. COntoh soal ini dapat membantu mengasah konsep tentang materi statistika. Terdapat data nilai ulangan Matematika kelas XI IPA 1 seperti pada tabel dibawah ini. Hitunglah median nilai ulangan Matematika kelas XI IPA 1. Berikut ini terdapat beberapa soal beserta pembahasan untuk materi peluang. Semoga dapat menambah pemahaman mengenai.

Siapa sih yang nggak mengagumi Bapak Proklamasi kita, Ir. Soekarno? Jasanya buesaaaar sekali bagi kemerdekaan Indonesia, Squad. Namun tahu nggak kalau ia pernah punya sahabat? Yap, namanya adalah Che Guevara, revolusioner sekaligus Menteri Perindustrian negara Kuba. Bayangin, sama gigihnya seperti Bung Karno, Che Guevara mengangkat perekonomian Kuba dari keadaan genting memakai prinsip penyelesaian program linear dalam matematika!

Fyi, penyelesaian program linear dipakai untuk optimasi atau mencari nilai yang paling efektif dari suatu proses. Nah, Che Guevara memanfaatkannya untuk mengolah industri-industri Kuba. Program linear membantu mengetahui berapa sih bahan baku yang harus dipakai suatu pabrik agar biaya produksi serendah mungkin tapi keuntungannya semaksimal mungkin. Penasaran kan gimana cara optimasi dengan menyelesaikan program linear? Cekidot!

Presiden Soekarno berdiskusi dengan Che Guevara (sumber: news.lewatmana.com)

Program linear biasanya berbentuk sistem pertidaksamaan linear dua variabel, Squad. Kamu harus mengingat kembali materi pertidaksamaan dan sistem pertidaksamaan linear dua variabel. Perlu kamu ketahui juga kalau optimasi dengan menyelesaikan program linear ada beberapa cara. Pastinya yang diterangkan di sini yang paling mudah dong. Yuk langsung cek langkah-langkah optimasi dengan menyelesaikan program linear.

Baca juga: Mencari Sisa dan Faktor Polinomial

Industri yang berkembang di Kuba saat itu adalah industri gula. Misalnya untuk membuat gula pada suatu pabrik diperlukan bahan baku tebu jenis X dan Y. Banyaknya tebu X dan tebu Y yang bisa diolah tidak lebih dari 6 peti kemas. Satu peti kemas untuk tebu X beratnya 2 ton dan satu peti kemas untuk tebu Y beratnya 3 ton.

Padahal, berat total peti kemas tebu X dan Y tidak boleh lebih dari 15 ton agar kendaraan pengangkut tidak overweight. Bila satu peti kemas tebu jenis X menghasilkan 3 ton gula dan satu peti kemas tebu jenis Y menghasilkan 4 ton gula, dengan semua syarat di atas, berapa maksimum berat gula yang dapat dihasilkan?

Masalah di atas adalah masalah yang bisa diselesaikan dengan optimasi dari menyelesaikan program linear, Squad. Kok bisa? Karena kita mencari banyaknya tebu X dan Y paling efektif untuk menghasilkan gula semaksimal mungkin walaupun terdapat seperti jumlah peti kemas tidak boleh lebih dari 6 dan berat totalnya tidak boleh lebih dari 15 ton. Langsung aja yuk kita ikuti langkah-langkah di atas.

1. Buat sistem pertidaksamaan linear dari masalah yang ada

Gimana tuh cara membuat sistem pertidaksamaannya? Slow Squad mudah kok. Coba lihat nih.

Caranya gimana hayo? Kita harus menggabungkan semua pertidaksamaan tersebut dalam satu grafik Squad. Ingat lho cara menggambar grafik yaitu cari dulu titik x saat y = 0 dan titik y saat x = 0 lalu kedua titik tersebut dihubungkan deh. Buka lagi deh materi persamaan garis lurus dan masalah polusi udara. Jangan lupa buat diarsir sesuai tanda pertidaksamaannya ya. Kalau lebih dari di atas dan kurang dari di bawah. Nanti jadi seperti ini deh.

Uji titik itu gimana sih? Gini, kita kan mau tau nih jumlah gula maksimum yang dihasilkan berapa. Satu peti kemas tebu X menghasilkan 3 ton gula. Padahal ada sebanyak x peti. Maka tebu X bisa menghasilkan 3x ton gula. Begitu pula dengan tebu Y. Ada sebanyak y peti dan masing-masing menghasilkan 4 ton gula. Maka tebu Y bisa menghasilkan 4y ton gula. Maka dihasilkan total gula sebanyak

Total gula = 3x + 4y

Nah, x dan y nya diisi berapa tuh? Kita isi dengan x dan y dari titik-titik kritis. Titik kritis adalah titik yang termasuk daerah penyelesaian sistem pertidaksamaan namun merupakan titik perpotongan 2 garis atau lebih. Coba deh cari dulu titik kritisnya.

Didapat deh 3 titik kritis tuh yaitu (0,5), (3,3), dan (6,0). Langsung aja masukin semuanya ke 3x + 4y

Lihat coba tuh. Saat dimasukkan x = 3 dan y = 3 maka 3x + 4y paling besar kan? Jadi agar berat gula yang dihasilkan maksimu, jumlah peti tebu jenis X haruslah sebanyak 3 peti kemas dan jenis Y haruslah sebanyak 3 peti kemas. Nanti dihasilkan deh gula seberat 21 ton.

Itu lah manfaat dari program linear. Kita bisa tahu harus berapa banyak bahan baku yang dipakai agar hasilnya bisa optimal. Kalau hasilnya optimal, untungnya gede juga dong. Pantas saja tuh Che Guevara bisa mengangkat perekonomian Kuba di zaman itu. Kalau kamu belajar yang rajin, kamu juga pasti bisa seperti dia Squad. Semangat 45!

Kalau kamu tertarik untuk belajar lebih dalam lagi, langsung aja daftar di ruangbelajar. Banyak banget lho video materi dan pembahasan soal. Tunggu apa lagi? Sikat Squad!

Artikel ini memberikan latihan soal SBMPTN HOTS Bahasa Inggris dan pembahasan 2019 untuk mata pelajaran bahasa Inggris

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Squad, walaupun masih belum ada keterangan pasti apakah mata pelajaran bahasa Inggris akan masuk ke SBMPTN 2019 mendatang, tidak ada salahnya bukan kamu mempelajarinya agar lebih siap dalam menghadapi soal SBMPTN HOTS. Yuk, langsung saja kita lihat latihan soal HOTS SBMPTN dan pembahasannya 2019 untuk pelajaran bahasa Inggris.

Questions 1 to 3 are based on the following text.

The latest round in an ongoing debate over global-warming trends claims that warming has indeed slowed down this century. An obvious slowing in the rise of global temperatures was recorded at the beginning of the twenty-first century. This was referred to as a 'hiatus' or a 'pause'. This hiatus was first observed several years ago. Climate-change skeptics have used this as evidence that global warming has stopped permanently. But in June the previous year, a study in science claimed that the hiatus was just an artifact which disappears when biases in temperature data are corrected.

Now a prominent group of researchers is countering that claim. They argue in Nature Climate Change that even after correcting these biases the slowdown was real. 'There is this mismatch between what the climate models are producing and what the observations are showing,' says lead author John Fyfe. 'We can't ignore it.' Fyfe uses the term 'slowdown' rather than 'hiatus'. He also stresses that it does not in any way weaken global-warming theory.

The study that questioned the existence of the slowdown corrected known biases in the surface temperature record maintained by the US National Oceanic and Atmospheric Administration (NOAA). The finding showed differences in temperature readings from ships and buoys. This effectively increased the record about warming. The researchers also extended the record to include 2014. This set a new record high for average temperatures.

Thomas Karl, director of National Centers for Environmental Information in Asheville, calculated the rate of global warming between 1950 and 1999 as being 0.113°C per decade. This was similar to the 0.116°C a decade calculated for 2000-14. This, Karl said, meant that an assessment done by the influential Intergovernmental Panel on Climate Change in 2013 showing that warming had slowed was no longer valid.

(Adapted from www.nature.com)

Topic: Extracting Core Information

Subtopic: Defining the Topic

1. The passage above mainly discusses about….

1. the hiatus observation was first carried out several years ago
2. the reason why global warming is slowing down in this century
3. global warming is a verifiable issue in the space of a decade
4. the contention about global warming and whether it is indeed slowing this period
5. the view of study in science that the hiatus is an artifact which vanishes

Answer: D

Perhatikan kalimat pertama pada paragraf ke-1 “The latest round in an ongoing debate over global-warming trends claims that warming has indeed slowed down this century.” inti kalimatnya mengatakan adanya perdebatan yang membahas tentang tren pemanasan global yang melambat abad ini. Maka topik dari teks di atas adalah (D) The contention about global warming and whether it is indeed slowing this period.

Topic: Understanding Implicit Information

Subtopic: Finding Contextual Meaning

2. The word “prominent” in paragraph 2 means….

1. well-known
2. promenade
3. shrewd
4. indolent
5. magnificent

Answer: A

Prominent (Terkenal) memiliki makna yang sama dengan pilihan jawaban (A) well-known. Sedangkan, pilihan jawaban (B) promenade artinya “perjalanan”, (C) shrewd berarti “cerdas”, (D) indolent memiliki arti “malas”, dan (E) magnificent artinya “sangat bagus”.

Topic: Paraphrasing Detailed Information

Subtopic: Understanding Specific Information

3. Why have some claimed that global warming a fabricated issue?

1. Because there’s no valid data to prove that global warming is real.
2. Since the existence of the slowdown corrected known biases in the surface temperature record upheld by the US NOAA.
3. As an assessment done on Climate Change presenting that warming had slowed was no longer valid.
4. For the researchers is countering that in Nature Climate Change even after correcting these biases the slowdown was real.
5. Because of the diversification in temperature readings from ships and buoys, the study found.

Answer: C

Del amitri members. Taking a tiny step backwards, Del Amitri did not top their previous outing this time, but they remained true to their musical cause. The fact that they sound a bit tired may mean that it is time to re-evaluate their journey. Tags: del amitri, twisted, 1995, flac.

Pilihan jawaban (C) merupakan opsi yang tepat karena pada paragraf ke-4 “This, Karl said, meant that an assessment done by the influential Intergovernmental Panel on Climate Change in 2013 showing that warming had slowed was no longer valid.” dikatakan bahwa perhitungan yang dilakukan oleh Panel Antarpemerintah pada Perubahan Iklim menunjukkan bahwa pemanasan telah melambat tidak lagi berlaku, yang mana artinya bahwa pemanasan global merupakan isu yang tidak benar.

The following text is for questions 4 to 5.

Over the last two decades, the use of ICT has been an important topic in education. On the one hand, studies have shown that ICT can enhance teaching and learning outcomes. For example, in science and mathematics education, scholars have documented that the use of ICT can improve students’ conceptual understanding, problem solving, and team working skills. Consequently, most curriculum documents state the importance of ICT and encourage school teachers to use them. However, teachers need to specifically trained in order to integrate ICT in their teaching.

Schools are known to be resistant to innovation and change, however, the spread of ICT is beginning to affect how teachers teach. One of the current issues about the use of ICT is how it is integrated into the curriculum. The curriculum document provide arguments for introducing ICT in the school setting. Therefore, schools expect that graduates from teacher education programs have a reasonable knowledge of how to use ICT. However, this may not be the case because most current teachers’ pre-service preparation, and subsequent in-service courses were designed by using traditional educational technology and settings. Thus, the participants in these courses are not familiar with the processes, interaction patterns, features, and possibilities of teaching learning processes based on ICT.

Effective development of pre-service teachers’ ICT proficiency does not seem to be a direct process, but is the one asking for a careful, complex approach. First, a need assessment is important to find out what ICT skills and knowledge teachers need at schools. Second, designers of teacher education programs should know the pre-service teachers’ perceptions of ICT and their attitudes toward ICT integration into curriculum. Third, teacher education programs need to consider the two typical arguments that support the ICT use in schools.

(Adapted from www.cjlt.ca)

Topic: Paraphrasing Detailed Information

Subtopic: Restating Phrases and Sentences

4. Which of the following best restates the sentence “Over the last two decades, the use of ICT has been an important topic in education. On the one hand, studies have shown that ICT can enhance teaching and learning outcomes.” in paragraph 1?

1. ICT usage has been a vital topic in education and studies indicate that ICT can develop teaching and learning upshot.
2. Studies have shown that ICT can enrich teaching and learning end result
3. The use of ICT has been an insignificant topic in education. Also, studies have shown that ICT can enhance teaching and learning outcomes.
4. Over the last two decades, the use of ICT has been an important topic in educational method.
5. Over the preceding two decades, studies have exposed that ICT can increase teaching and learning outcomes.

Answer: A

Dalam pernyataan “Selama dua dekade terakhir, penggunaan ICT telah menjadi topik penting dalam pendidikan. Di satu sisi, penelitian telah menunjukkan bahwa TIK dapat meningkatkan hasil pengajaran dan pembelajaran.” dapat dinyatakan kembali oleh opsi (A) ICT usage has been a vital topic in education and studies indicate that ICT can develop teaching and learning upshot.

Topic: Extracting Core Information

Subtopic: Comprehending Main Ideas

5. Based on the passage, paragraph 1 most likely discusses….

1. educational growth in the last two decades
2. the development of education by using ICT
3. the advantages of using ICT in the learning process
4. teachers need to be trained in order to integrate ICT in their teaching
5. ICT and education in today’s learning development

Answer: B

Pertanyaan soal ini intinya menanyakan topik paragraf ke-1. Paragraf ke-1 topiknya membahas penggunaan TIK telah menunjukkan bahwa TIK dapat meningkatkan hasil pengajaran dan pembelajaran “On the one hand, studies have shown that ICT can enhance teaching and learning outcomes.” itu artinya adanya pengembangan pendidikan dengan menggunakan TIK. Maka pilihan jawaban (B) the development of education by using ICT merupakan opsi yang tepat.

Question number 6 to 8 are based on the following text.

Sleepiness after eating is a response of the body to chemical changes during the digestion process. This is normal and it happens to everybody. However, if sleepiness occurs every time after eating and obstructs your ability to function, this may be a concern. Sleepiness after eating is caused by many factors, such as the type of food you consume, messy sleeping habits, your health condition and so forth. The body requires energy to function and this energy is obtained through food. Post-eating, the body releases hormones such as amylin, glucagon and cholecystokinin. These hormones increase blood sugar levels, creating a feeling of fullness and producing insulin that will be streamed through cell tissues and provide energy for them. At the same time, the brain releases serotonin that causes drowsiness.

Moreover, food also influences melatonin production in the brain. This is the hormone that is responsible for sleepiness post-meal. Some foods that are rich in protein, such as meat, poultry, eggs, fish, spinach, tofu, cheese and soybeans can trigger more drowsiness than others. Additionally, foods containing carbohydrates also help produce serotonin and tryptophan amino acids found in the brain. This is the reason why you feel sleepy after eating carbohydrate-rich foods.

Overeating can also cause sleepiness. Post-meal, the body streams more blood to the digestive system to better digest foods in massive amounts. This causes a temporary blood and nutrients shortage in the brain. To prevent post-meal drowsiness, it’s better to eat a balanced diet containing vegetables, grains and good fats to provide continuous energy. Drink lots of water and limit your sugar intake.

Bad sleeping patterns can also cause sleepiness after eating. After a meal, the body feels full and relaxed, making the body feel like it is resting, resulting in a feeling of sleepiness, particularly if you didn’t get a good night’s sleep the night before. To avoid this, improve your sleeping habits to prevent stress. Engaging in regular physical exercise can help you get a good night’s sleep. It is recommended that you avoid napping if you are having trouble sleeping at night.

(Adapted from www.thejakartapost.com)

Topic: Understanding Implicit Information

Subtopic: Author-related Questions

6. What is the author’s purpose in writing the passage?

1. To discuss the amount of food to consume so as not to feel sleepy
2. To inform the readers about the factors of sleepiness after eating
3. To argue the effect of eating too much foods for the brain
4. To tell the readers the benefit of eating certain foods
5. To investigate what causes drowsiness after overeating

Answer: B

Tujuan penulis dalam menulis teks di atas adalah untuk menginformasikan faktor kantuk setelah makan.

1. Sleepiness after eating is a response of the body to chemical changes during the digestion process.
2. Moreover, food also influences melatonin production in the brain. This is the hormone that is responsible for sleepiness post-meal.
3. Overeating can also cause sleepiness.
4. Bad sleeping patterns can also cause sleepiness after eating. After a meal, the body feels full and relaxed, making the body feel like it is resting, resulting in a feeling of sleepiness, particularly if you didn’t get a good night’s sleep the night before.

Maka pilihan jawaban (B) To inform the readers about the factors of sleepiness after eating merupakan opsi yang tepat.

Topic: Understanding Implicit Information

Subtopic: Author-related Questions

7. By writing the sentences in paragraph 2, the author intends to tell the readers about….

1. foods that are rich in protein, such as meat, eggs, fish, tofu, cheese and soybeans can generate more drowsiness
2. overeating protein and carbohydrate-rich foods obstructs your brain’s ability to function well
3. the reason why carbohydrate-rich foods make you feel sleepy
4. food combinations containing tryptophan amino acid and carbohydrates make you feel drowsy
5. the hormone melatonin production in the brain is responsible for sleepiness after eating

Answer: D

Paragraf ke-2 penulis intinya bermaksud untuk memberitahu pembaca bahwa kombinasi makanan yang mengandung asam amino triptofan (protein) dan karbohidrat membuat Anda merasa mengantuk (Additionally, foods containing carbohydrates also help produce serotonin and tryptophan amino acids found in the brain. This is the reason why you feel sleepy after eating carbohydrate-rich foods.). Maka pilihan jawaban (D) food combinations containing tryptophan amino acid and carbohydrates make you feel drowsy merupakan opsi yang tepat.

Topic: Understanding Implicit Information

Subtopic: Predicting Paragraph

8. It can be predicted from the passage that….

1. the finer you manage your sleep, the more lethargic you feel
2. the more fish you eat, the better it is for the brain
3. the less you eat carbohydrate-rich foods, the less you will feel drowsy
4. the less meat you eat, the more you will feel drowsy
5. the less you consume protein and carbohydrates, the better it is for the body

Answer: C

Dari kalimat “This is the reason why you feel sleepy after eating carbohydrate-rich foods.” dapat diprediksikan bahwa semakin sedikit Anda mengonsumsi makanan yang kaya karbohidrat, maka rasa kantuk akan berkurang. Maka pilihan jawaban (C) the less you eat carbohydrate-rich foods, the less you will feel drowsy merupakan opsi yang tepat.

The text below is for queries 9 to 10

Indonesia is the world’s third-largest coffee producer and exporter, after Brazil and Vietnam. National coffee output has grown over the past decades, albeit not in a linear fashion as harvests fluctuate strongly from one year to another depending on the weather. With per-capita coffee consumption on the rise both in Indonesia and the wider region, there is obvious room for further growth, but there is also an obvious need for investment. The capital required to take Indonesia’s coffee industry to the next level presents appealing prospects for investors, while the country’s burgeoning coffee culture also brings opportunities for foreign exporters.

Indonesia’s tropical climate produces almost ideal conditions for planting coffee. Today, most Indonesian coffee comes from Sumatra, but Sulawesi and Kalimantan, the Lesser Sunda Islands of Bali, Sumbawa and Flores as well as the country’s easternmost region of Papua all contribute to national output. Robusta coffee makes up more than three quarters of Indonesia’s produce; the remainder is of the milder Arabica type. The numerous coffee-growing regions in the country produce beans of distinct flavors and properties, and a number of highland Arabica coffees from Indonesia are recognized by aficionados the world over.

Indonesian coffee exports rose from 336,840 tonnes (or 5,614,000 60-KG bags) in crop year 2000/2001 to 656,400 tonnes (10,940,000 bags) in 2012/2013, according to data collated by the International Coffee Organization. Total production over the same period increased from 419,220 tonnes to 763,800 tonnes. At present, the principal destinations for Indonesian coffee are the US, Japan and Western Europe (particularly Germany), but Indonesia is well placed to capitalize on the fast-rising demand in the ASEAN region and in China.

Indonesian per-capita consumption of around 1.2 kg in 2012 pales against more than 4 kg in the US, around 7 kg in the world’s number one coffee producer Brazil and more than 10 kg in various European countries. But with Indonesian per-capita consumption having already doubled in just a few years, domestic demand looks to be on a fast growth trend. This puts the world’s fourth-most populous country on course to become a leading coffee market. Local demand is driven by the lifestyle changes that accompany urbanization and economic development. Caffeine consumption tends to increase when a larger part of the labor force works in an office environment.

(Adapted from www.gbgindonesia.com)

Topic: Extracting Core Information

Subtopic: Summarizing The Passage

9. What is the best summary of the passage?

1. The primary destinations for Indonesian coffee export are the US, Japan and Western Europe
2. Total production of Indonesian coffee over the same period has increased
3. Indonesia is well placed to capitalize on the fast-rising demand in the ASEAN region
4. The various coffee-growing in the country produce beans of distinct flavors
5. Indonesia’s coffee growing and Indonesia’s coffee industry needs growth capital

Answer: E

Ringkasan yang tepat dari teks di atas adalah pilihan jawaban (E) Indonesia’s coffee growing and Indonesia’s coffee industry needs growth capital yang bermakna “Perkembangan kopi Indonesia dan industri kopi Indonesia perlu pertumbuhan modal” karena kalimat ini mewakili isi dari teks di atas sebagaimana yang tercantum di kalimat utama paragraf pertama “Indonesia is the world’s third-largest coffee producer and exporter, after Brazil and Vietnam. National coffee output has grown over the past decades, albeit not in a linear fashion as harvests fluctuate strongly from one year to another depending on the weather. With per-capita coffee consumption on the rise both in Indonesia and the wider region, there is obvious room for further growth, but there is also an obvious need for investment.”

Topic: Paraphrasing Detailed Information

Subtopic: Understanding Specific Information

10. What can be inferred from paragraph 3 in the passage?

1. The coffee export has decreased in several years
2. Total production deducted from 419,220 tonnes to 763,800 tonnes
3. Indonesian coffee exports increased from 2000/2001 to 2012/2013
4. Indonesia is in a good site to take advantage of fast-rising demand in ASEAN
5. The US, Japan and Western Europe are the destination for Indonesian coffee

Answer: C

Dari paragraf ke-3 bisa disimpulkan bahwa ekspor kopi Indonesia telah meningkat dari tahun 2000/2001 sampai tahun 2012/2013. Ini ada pada awal kalimat paragraf ke-3 tersebut. Maka pilihan jawaban (C) Indonesian coffee exports increased from 2000/2001 to 2012/2013 merupakan opsi yang tepat.

Mudah dimengerti 'kan Squad? Jangan lupa ya untuk menyimak latihan soal HOTS SBMPTN lainnya di ruangbaca, atau menonton video pembahasan soal-soal SBMPTN di ruangbelajar.