Judul: Perancangan Alat dan Tata Letak Industri Minyak Serum dan Produk Sampingnya Berbasis Buah Nyamplung pada Skala Industri Menengah
Abstrak: Minyak nyamplung (Calophyllum inophyllum) merupakan minyak hasil ekstraksi dari biji nyamplung secara mekanik atau dengan pelarut. Aktivitas senyawa aktif dalam minyak yang memiliki beragam khasiat baik bagi kesehatan kulit, menjadikan minyak hanya sebagai obat-obatan tradisional. Salah satu upaya solusi untuk meningkatkan nilai tambah yaitu dengan melakukan pengembangan produk yang memiliki nilai jual lebih tinggi. Minyak serum merupakan salah satu pengembangan produk yang cocok. Transformasi produk dari obat tradisional menjadi minyak serum memerlukan perancangan teknologi proses yang tepat. Teknologi proses yang baik juga memperhatikan pemilihan peralatan yang sesuai. Penelitian ini dilakukan untuk merancang peralatan dan tata letak industri minyak serum dan produk sampingnya berbasis buah nyamplung pada skala industri menengah. Pemilihan peralatan yang digunakan menyesuaikan kebutuhan tiap lini produksi. Penentuan kapasitas peralatan berdasarkan kebutuhan operasional dan kapasitas kerja. Ada tiga alternatif skema proses produksi minyak serum pada penelitian ini dimana setiap alternatif merupakan kombinasi dua proses yang berbeda, yaitu cold dan hot hydraulic press, cold hydraulic press dan ekstraksi pelarut biner, hot screw press dan ekstraksi pelarut biner. Skema 1 memerlukan luas area 280 m2 dengan 8 jenis peralatan berbeda. Skema 2 memerlukan luas area 340 m2 dengan 19 jenis peralatan berbeda. Skema 3 memerlukan luas area 340 m2 dengan 18 jenis peralatan berbeda. Tata letak industri minyak serum dibuat menggunakan metode Systematic Layout Planning (SLP). Pemilihan lokasi pendirian industri berada di Kawasan Industri Jababeka, Kabupaten Bekasi, Provinsi Jawa Barat., Calophyllum Oil is an oil extracted from calophyllum seeds mechanical or solvent extraction processes. The activity of the active compounds in the oil which have a variety of good properties for skin health, it just makes the oil become a traditional medicine. One solution to increase added value of the products is to develop products that have a higher selling value. Serum oil is one suitable product development. Product transformation from traditional medicine to serum oil requires the design of good process technology. Good process technology also needs a good selection of appropriate equipment. This research was conducted to design the equipment and layout of the serum oil industry and by-products based on calophyllum fruit on a medium industrial scale. The selection of equipment is considered by the needs of each production line. The determination of an equipment capacity based on operational needs and work capacity. There were three alternatives for the serum oil production process in this study where each alternative was a combination of two different processes, namely cold and hot hydraulic press, cold hydraulic press and binary solvent extraction processes, hot screw press and binary solvent extraction processes. Alternative one required an area production of 280 m2 with 8 different types of equipment production processes. For alternative two required an area production of 340 m2 with 19 different types of equipment production processes. For alternative three required an area production of 340 m2 with 18 different types of equipment production processes. The layout of the serum oil industry used the Systematic Layout Planning (SLP) method. The location of the industrial establishment was chosen in the Jababeka Industrial Estate, Bekasi Regency, West Java Province.
Keyword: nyamplung, tata letak, rancangan alat

Judul: Business Analysis on Serum Oil Industry and By-Products Based on Nyamplung Fruit on a Medium Industrial Scale
Abstrak: Pemanfaatan tanaman untuk produk kosmetik kulit merupakan hal yang perlu dikembangkan di Indonesia. Hal ini didasari dengan melimpahnya tanaman berkhasiat yang belum dimanfaatkan secara maksimal untuk produk kosmetika perawatan kulit. Nyamplung (Calophyllum inophyllum) merupakan salah satu tanaman berkhasiat tinggi yang prospektif untuk dikembangkan. Faktor utamanya yaitu pada produkminyak nyamplung memiliki kandungan senyawa aktif dan beragam manfaat. Minyak nyamplung dapat diproduksi melalui proses ekstraksi secara mekanik dan atau dengan pelarut. Selain minyak, terdapat produk samping berupa biopelet dan pakan ternak yang akan menambah pendapatan. Teknologi proses produksi minyak serum yang diuji dalam penelitian ini menggunakan bahan baku biji nyamplung segar dengan tiga skema proses produksi dimana setiap skema melakukan dua kali proses ekstraksi minyak dengan kombinasi yang berbeda, yaitu cold dan hot hydraulic press, cold hydraulic press dan pelarut biner, hot screw press dan pelarut biner. Penelitian ini dilakukan untuk merancang model bisnis menggunakan metode Business Model Canvas (BMC) yang mencakup produk, segmentasi konsumen, rancangan keuangan, dan kegiatan operasional, serta menganalisis studi kelayakan untuk setiap skema. Hasil analisis biaya dari masing-masing proses produksi pada skema 1 mendapatkan nilai biaya investasi sebesar Rp 2.714.434.262 dengan besar pendapatan sebesar Rp 4.049.062.489. Untuk skema 2 memperoleh biaya investasi senilai Rp 3.118.791.515 dengan pendapatan sebesar Rp 5.208.184.137. Terakhir pada skema 3 memperoleh biaya investasi sebesar Rp 3.033.466.092 dengan pendapatan Rp 5.924.724.490. Berdasarkan studi kelayakan yang telah dilakukan dengan 4 kriteria yaitu Net Present Value (NPV), B/C ratio, Payback Period (PBP), dan Return on Investment (ROI) memperoleh hasil layak pada ketiga skema tersebut. Dengan demikian industri minyak serum untuk ketiga skema tersebut layak untuk dibangun dan dioperasikan., Utilization on plants for skin cosmetic products is something that needs to be developed in Indonesia. This is based on the abundance on nutritious plants that have not been used optimally for skin care cosmetic products. Calophyllum is one on the highly nutritious plants that are prospective to be developed. The main factor is Calophyllum oil products contain active compounds and various benefits. Calophyllum oil can be produced through mechanical and/or solvent extraction processes. In addition to oil, there are by-products in the form on biopelets and animal feed that will increase income. Serum oil production process technology tested in this research used fresh nyamplung seeds as raw material with three alternative production processes where each alternative performed two oil extraction processes with different combinations, namely cold and hot hydraulic press, cold hydraulic press and binary solvent, hot screw press and binary solvent. This research was conducted to design a business model using the Business Model Canvas (BMC) method which includes products, consumer segmentation, financial design, and operational activities, as well as analyzing a feasibility study for each alternative. The results on the cost analysis on each production process in alternative 1 got an investment cost on Rp 2.714.434.262 with a large income on Rp 4.049.062.489. For alternative 2 obtained an investment cost on Rp 3.118.791.515 with an income on Rp 5.208.184.137. Finally, in alternative 3, the investment cost was Rp 3.033.466.092 with an income on Rp 5.924.724.490. Based on the feasibility study that had been carried out with 4 criteria,
Keyword: minyak serum, nyamplung, ekstraksi, business model canvas, kelayakan

Judul: Penentuan Nilai Eigen dan Vektor Eigen dari Matriks Tridiagonal 2-Toeplitz dengan Pendekatan Polinomial Chebyshev
Abstrak: The eigenvalues and eigenvectors of a matrix can be determined by finding its characteristic polynomials. The characteristic polynomials of a tridiagonal 2-Toeplitz matrix is shown to be closely connected to polynomials which satisfy the Chebyshev recurrence relationship. If the order of the matrix is odd, then the eigenvalues are found explicitly in terms of the Chebyshev zeros and the eigenvectors are found in terms of the polynomials satisfying the recurrence relationship. For even ordered matrices, the situation is more complicated. The problem in these cases is that although the Chebyshev recurrence formula is still applied, its initial values are not generating Chebyshev polynomials
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