Petunjuk : Pergunakanlah garis selidik atau titik pojok (sudut) untuk menyelesaikan permasalahan berikut.
01. Rokok jenis “ arma” yang harganya 200 dukat per bungkus dijual dengan laba 40 dukat per bungkus, sedangkan rokok jenis “armin “ armin”” yang harganya 100 dukat per bungkus dijual dengan laba 30 dukat per bungkus. Seorang pedagang yang mempunyai modal 80.000 dukat, dan kiosnya mampu menampung 500 bungkus rokok. Agar pedagang tersebut memperolah laba maksimum, tentukan : 1.
Berapa Ber apa bun bungku gkuss rokok rokok yan yang g harus harus dib dibeli eli..
2. Ber Berapa apa keu keuntu ntunga ngan n mak maksim simumn umnya ya 02. Seorang penjaja kue membeli kue A dengan harga 100 cent, kemudian kemudian menjualnya dengan harga 130 cent per potongnya. Sedangkan kue B dibeli dengan harga 200 cent, dan dijual 220 cent. Jika modal yang dimiliki hanya 4000 cent, dan setiap hari hanya mampu menjual 30 kue, maka laba maksimal setiap harinya adalah ? 03. Untuk dapat diterima di suatu PT ternama, seorang calon harus lulus tes matematika matematika tidak kurang dari 8, tes logika tidak kurang dari 5. Si Steven memiliki hasil ujian dimana jumlah dua kali nilai matematika dan tiga kali nilai logika sama denga 30. Menurut anda diterima atau tidak calon tersebut ? (=ditolak, karena ? ) 04. Seorang saudagar menjual dua jenis jenis barang A dan B. Harga pembelian barang A Rp Rp 1000 per satuan, barang B Rp 400 per satuan. Modal yang dmiliki Rp 250.000, sementara jumlah barang yang dibeli tidak lebih 400 satuan. Jika keuntungan barang A adalah dua kali keuntungan barang B, maka agar diperoleh keuntungan maksimal, pedagang harus membeli barang sebanyak ? 05. Seorang yang ingin sehat bermaksud untuk minum minum sedikitnya 36 sat vitamin A per hari, 28 sat vit C dan 32 sat vitamin D. Multivitamin jenis pertama berharga 3 sat uang menyediakan 2 sat vitamin A per hari, 2 sat vitamin C dan 8 sat vitamin D. Multivitamin jenis kedua berharga 4 sat uang menyediakan 3 sat vitamin A per hari, 2 sat vitamin C dan 2 sat vitamin D. Tentukan jumlah vitamin yang harus diminum agar kebutuhan akan vitamin terpenuhi. 06. Sebuah perusahaan truk mempunyai mempunyai 2 jenis truk. Jenis I mempunyai 20 m 3 kotak berpendingin dan 40 m3 tanpa pendingin. Kendaraan jenis II mempunyai 30 m 3 kotak pendingin, dan 30 m 3 tanpa pendingin. Petani ingin mengirim 900 m 3 sayuran yang harus dikirim dengan cara mendinginkan, dan
1200 m3 tanpa harus didinginkan. Tentukan jumlah truk yang harus disewa agar ongkos sewa minimum, jika : 1.
Ongkoss truk jeni Ongko jeniss I adalah adalah 30 sat.ua sat.uang, ng, dan dan jenis jenis II adalah adalah 40 40 sat.uang sat.uang
2. Ongko Ongkoss truk jenis jenis I adalah adalah 20 sat.ua sat.uang, ng, dan dan jenis jenis II adalah adalah 30 sat.uang sat.uang 07. Seorang petani memerlukan 3 jenis jenis zat kimia A,B, dan C masing-masing sebesar 10,12, dan 12 satuan per satuan luas. Produk dalam bentuk kering memuat zat A,B, dan C masing-masing 5,2 dan 1 satuan per karton. Produk dalam bentuk basah memuat zat A,B, dan C masing-masing 1,2 dan 4 per botol. Jika produk cair dijual dengan harga 3 satuan uang per botol dan produk pr oduk kering dijual 2 satuan uang per karton, tentukan jumlah produk yang harus dibeli dengan ongkos sekecil mungkin. 08. Suatu perusahaan penambangan mempunyai mempunyai 2 tempat. Tiap hari, penambangan penambangan A menghasilkan masing-masing 1 ton, 3 ton dan 5 ton biji besi kualitas kurang,sedang dan baik. Penambangan B menghasilkan masing-masing 2 ton biji besi. Perusahaan memerlukan masing-masing 80 ton, 160 ton dan 200 ton biji besi berkualitas kurang, sedang dan baik. Berapa hari penambangan tersebut harus bekerja agar ongkos yang dikeluarkan sekecil mungkin jika ongkos penambangan 200 satuan uang per hari. 09. Pedagang roti memiliki tiga tiga bahan A,B, dan C masing-masing masing-masing sebanyak 150,90 dan 150 satuan. Roti polos memerlukan bahan A,B, dan C masing-masing sebanyak 1,1, dan 2 satuan, sedangkan kue memerlukan bahan A,B, dan C masing-masing sebanyak 5,2, dan 1 satuan. Tentukan jumlah roti dan kue yang harus dibuat agar pendapatan maksimum. 10. A plant makes aluminum and copper wire. Each pound of aluminum wire requires 5 kwh of electricity electricity and 0.25 hour of labor. Each pound of copper wire requires 2 kwh of electricity and 0.5 hour of labor. Production of copper wire is restricted by the fact that raw materials are available to produce at most 60 lbs/ day. Electricity is limited to 500 kwh/ day and labor to 40 person – hour/ day. If the profit from aluminum wire is $ 0.25/lb, and the profit from copper is $ 0.40/ lb., how much of each should be produced to maximize profit and what is the maximum profit? 11. A farmer has a 320 acre farm on which she she plants two crops: corn and soybeans. soybeans. For each acre of corn planted, her expenses are $ 50 and for each acre of soybeans planted, her expenses are $ 100. Each acre of corn requires 100 bushels of storage and yields a profit of $ 60; each acre of soybeans requires 40 bushels of storage and yields a profit of $ 90. If the total amount of storage space available is 19,200 bushels and the farmer has only $ 20,000 on hand, how many acres of each crop should she plant in order to maximize her profit? What will her profit be if she follows f ollows this strategy?
12. A potter is making cups and plates. It takes her 6 minutes to make a cup and 3 minutes to make a plate. Each cup uses 0.75 lb of clay and each plate uses one lb of clay. She has 20 hours available for making the cups and plates and has 250 lb of clay on hand. She makes a profit of $ 2 on each cup and $ 1.50 on each plate. How many cups and how many plates should she make in order to maximize her profit?
Linear Programming Problems
1.
A farmer farmer has 10 acres acres to plant plant in wheat wheat and and rye. He has to plant plant at least least 7 acres. acres. However, However, he he has only $1200 to spend and each acre of wheat costs $200 to plant and each acre of rye costs $100 to plant. Moreover, the farmer has to get the planting done in 12 hours and it takes an hour to plant an acre of wheat and 2 hours to plant an acre of rye. If the profit is $500 per acre of wheat and $300 per acre of rye how many acres of each should be planted to maximize profits?
2. A gold processo processorr has two sources sources of gold gold processor, processor, source source A and and source B. B. In order to keep keep his plant running, at least three tons of ore must be processed each day. Ore from source A costs $20 per ton to process, and ore from source B costs $10 per ton to process. Costs must be kept to less than $80 per day. Moreover, Federal Regulations require that the amount of ore from source B cannot exceed twice the amount of ore from source A. If ore from source A yields 2 oz. of gold per ton, and ore from source B yields 3 oz. of gold per ton, how many tons of ore from both sources must be processed each day to maximize the amount of gold extracted subject to the above constraints? 3. A publisher publisher has orders orders for 600 copies copies of a certain certain text text from San Franci Francisco sco and 400 copies copies from from Sacramento. The company has 700 copies in a warehouse in Novato and 800 copies in a warehouse in Lodi. It costs $5 to ship a text from Novato to San Francisco, but it costs $10 to ship it to Sacramento. It costs $15 to ship a text from Lodi to San Francisco, but it costs $4 to ship it from Lodi to Sacramento. How many copies should the company ship from each warehouse to San Francisco and Sacramento to fill the order at the least cost? 4. A calculator calculator company company produces produces a scientifi scientificc calculator calculator and a graphing graphing calculator. calculator. Long-t Long-term erm 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 200scientific 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? 5.
You need need to buy some filing filing cabine cabinets. ts. You know know that Cabine Cabinett X costs $10 $10 per unit, unit, requires 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 storage volume?
Hints: 1.
Every group group just just solves solves three three problems; problems; but you you must must answer answer question question number number four. four.
2. Due dat date: e: 31 Aug August ust 200 2009 9 by ema email. il.
Steps: 1.
Defi De fine ne yo your ur un unkn know owns ns
2. Det Determ ermine ine the the mathem mathemati aticc model model of each each problem problem 3. Exp Expres resss the obje objecti ctive ve and and the cons constra traint ints. s. 4. Write the cons constrain traints ts and and the objec objective tive func function. tion. 5.
Graph the the solution solution area area of the the problems, problems, and find find the feasib feasible le corner corner points points
6. Evalua Evaluate te the objec objective tive functi function on in all all of the feasib feasible le corner corner points points
