12
Mar
10

Model Matematika Yang Berkaitan dengan Progam Linier

Progam linier adalah proses menghubungkan beberapa pertaksamaan dari beberapa situasi, dan mencari solusi terbaik dengan kondisi yang ada. Contoh yang sering memerlukan progam linier adalah masalaha keterbatasan materi dan tenaga kerja, dan menentukan produksi terbaik untuk profit yang maksimal terhadap kondisi tersebut.

Dalam “dunia nyata”, progam linier adalah bagian sangat penting dari bidang matematika yang dikenal dengan nama “teknik pengoptimuman”. Bidang ilmu (minimal penerapan hasil darinya) digunakan tiap hari dalam pengorganisasian dan mengalokasian sumber daya. Sistem seperti itu (di dunia nyata) memiliki banyak (bahkan ratusan atau lebih) variabel. Dalam aljabar, kamu hanya bekerja dengan masalah kasus sederhana dua variabel.

Proses umum untuk menyelesaikan masalah progam linier (dua variabel) adalah menggambar pertidaksamaan (batasan) ke bidang xy (daerah feasible). Kemudian kamu temukan koordinat dari daerah feasible (yakni titik perpotongan dari berbagai garis), dan mengetest titik-titik tersebut kedalam rumus/fungsi tujuan (persamaan optimum) yang mana kamu cari yang menghasilkan nilai tertinggi atau terendah.

BERIKUT BEBERAPA PERMASALAHAN PROGAM LINIER

Masalah Pertama

At a certain refinery, the refining process requires the production of at least two gallons of gasoline for each gallon of fuel oil. To meet the anticipated demands of winter, at least three million gallons of fuel oil a day will need to be produced. The demand for gasoline, on the other hand, is not more than 6.4 million gallons a day.

If gasoline is selling for $1.90 per gallon and fuel oil sells for $1.50/gal, how much of each should be produced in order to maximize revenue?

Masalah Kedua

A calculator company produces a scientific calculator and a graphing calculator. Long-term projections indicate an expected demand of at least 100 scientific and 80 graphing calculators each day. Because of limitations on production capacity, no more than 200 scientific and 170 graphing calculators can be made daily. To satisfy a shipping contract, a total of at least 200 calculators much be shipped each day.

If each scientific calculator sold results in a $2 loss, but each graphing calculator produces a $5 profit, how many of each type should be made daily to maximize net profits?

Masalah Ketiga

You need to buy some filing cabinets. You know that Cabinet X costs $10 per unit, requires six square feet of floor space, and holds eight cubic feet of files. Cabinet Y costs $20 per unit, requires eight square feet of floor space, and holds twelve cubic feet of files. You have been given $140 for this purchase, though you don’t have to spend that much. The office has room for no more than 72 square feet of cabinets. How many of which model should you buy, in order to maximize shorage volume?

Masalah Keempat

In order to ensure optimal health (and thus accurate test results), a lab technician needs to feed the rabbits a daily diet containing a minimum of 24 grams (g) of fat, 36 g of carbohydrates, and 4 g of protien. But the rabbits should be fed no more than five ounces of food a day.

Rather than order rabbit food that is custom-blended, it is cheaper to order Food X and Food Y, and blend them for an optimal mix. Food X contains 8 g of fat, 12 g of carbohydrates, and 2 g of protein per ounce, and costs $0.20 per ounce. Food Y contains 12 g of fat, 12 g of carbohydrates, and 1 g of protein per ounce, at a cost of $0.30 per ounce.

What is the optimal blend?

Masalah Kelima

Sometimes you’ll have more than just two things to deal with. The next example has three things to juggle; the next page provides an example of juggling four things.

You have $12,000 to invest, and three different funds from which to choose. The municipal bond fund has a 7% return, the local bank’s CDs have an 8% return, and the high-risk account has an expected (hoped-for) 12% return. To minimize risk, you decide not to invest any more than $2,000 in the high-risk account. For tax reasons, you need to invest at least three times as much in the municipal bonds as in the bank CDs. Assuming the year-end yields are as expected, what are the optimal investment amounts?

Masalah Keenam

A building supply has two locations in town. The office receives orders from two customers, each requiring 3/4-inch plywood. Customer A needs fifty sheets and Customer B needs seventy sheets.

The warehouse on the east side of town has eighty sheets in stock; the west-side warehouse has forty-five sheets in stock. Delivery costs per sheet are as follows: $0.50 from the eastern warehouse to Customer A, $0.60 from the eastern warehouse to Customer B, $0.40 from the western warehouse to Customer A, and $0.55 from the western warehouse to Customer B.

Find the shipping arrangement which minimizes costs.

Masalah Ketujuh

Pabrik Gamatika memproduksi bola kaki dan bola basket, yang akan dijual ke vendor-vendor diseluruh indonesia. Kemampuan pabrik adalah memproduksi 500 bola kaki maksimum dalam sehari, dan maksimum memproduksi 500 bola basket setiap hari. Kulit sapi sebagi pelapis luar bola dipotong dari lembaran kulit sapi yang ada. Setiap bola kaki membutuhkan lima satua luas kulit sapi (termasuk limbahnya) sementara bola basket butuh enam satuan luas kulit sapi (termasuk limbahnya). Gamatika memiliki 3600 satuan luas kulit sapai tiap harinya.
Sementara waktu pembuatan se bola kaki adalah satu menit, sementara bola basket dua menit. Sehari waktu produksi yang dibutuhkan adalah 960 menit. Keuntungan dari satu bola kaki adalah 7 dan satu bola basket adalah 10 (dalam satuan ribu rupiah). Optimalkan keuntungan pabrik !!

 

PENTING !!

KELOMPOK 1-3 diberi Kesempatan untuk rebutan memilih terlebih dahulu !!


13 Responses to “Model Matematika Yang Berkaitan dengan Progam Linier”


  1. March 12, 2010 at 4:00 am

    Masalah Ketujuh tidak boleh dipilih kelompok 1-3
    Jika ada kelompok 4-7 yang meilih problem duluan kemudian kelompok 1-3 memilih progam yang sama maka, yang sah adalah kelompok 1-3.
    Dilarang memilih dua kali dalam satu komentar.

  2. March 12, 2010 at 10:27 pm

    dengan ini kelompok 1 menyatakan bahwa tugas yang diambil adalah nomor 4 dengan kesiapan menanggung resiko soal….

  3. March 13, 2010 at 6:53 am

    kami kelompok 2 memilih masalah nomor 3
    atas perhatiannya kami sampaikan terima kasih

  4. March 14, 2010 at 3:32 am

    kami kelompok 3 memilih masalah kedua pak..

  5. 5 ung08
    March 14, 2010 at 10:09 am

    ooo Bapak !

    kelompok ung kelompok 9 ngambil masalah no 7 nih..

    hehhehehehehe

  6. March 15, 2010 at 12:48 am

    Bunda……
    Qta kelompok 7…
    jdi ngambil soal no 7……

  7. 9 mEidatuzzahra
    March 15, 2010 at 8:16 am

    Mr.aDit,,,
    Our group of four took over the number one..
    okeeeeeyyyyy??
    ^^

  8. 10 devi
    March 15, 2010 at 11:56 am

    pak,,,
    kelompok 5 pilih soal no 5…..

  9. March 17, 2010 at 10:31 am

    pak klompok ngalah sma kelompok yg lain,,,jadinya kami pilih yg mana yg di sisain,,,jadinya ngmbil masalah yg keenam pak…..

  10. March 17, 2010 at 10:32 am

    ow ya kami klompok 6 pak….

  11. 13 mulyadi
    September 29, 2016 at 11:45 am

    yang termasuk sistem matematika apa aja materi nya tu?


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s


1_502554913l

Current CO2 Level in the Atmosphere

yang sudah mampir

  • 200,745 gamatika-ers

Kategori Tulisan

No Smoking

Lagi Online

Arsip

March 2010
M T W T F S S
« Jan   May »
1234567
891011121314
15161718192021
22232425262728
293031  

%d bloggers like this: