Judul: Process and Product Design of Jelly Candy from Rejected  Calina Papaya
Abstrak: KN Jaya Farm menghasilkan pepaya afkir terlalu matang dalam jumlah besar yang berpotensi diolah menjadi produk pangan untuk meningkatkan nilai tambahnya. Penelitian ini bertujuan untuk mendapatkan desain proses dan produk permen jeli pepaya, serta gambaran penerimaan konsumen terhadap produk yang dihasilkan. Desain proses dilakukan pada titik proses utama pengolahan produk. Proses pemasakan bahan dilakukan pada suhu 80°C selama 5 menit. Proses pengeringan dilakukan pada suhu 50°C selama 24 jam, kemudian dilanjutkan pengeringan pada suhu 70°C selama 2 jam. Desain produk dilakukan melalui pengembangan formulasi berdasarkan hasil uji organoleptik, pengujian kualitas, dan desain kemasan produk. Formulasi terbaik untuk permen jeli diperoleh dengan komposisi bahan sebanyak 1200 gram pepaya calina, 72 gram bubuk jeli, 18 gram pektin, 120 gram air, 12 gram kolagen, 360 gram gula pasir, 12 gram perisa, 0,6 gram pewarna, 3,6 gram asam sitrat, dan 24 gram gula halus. Kemasan produk yang digunakan berupa toples plastik. Hasil penerimaan konsumen menunjukkan kelayakan jual dan minat beli produk permen jeli yang disetujui oleh lebih dari 90% responden. KN Jaya Farm produces a large quantity of overripe papayas that have potential to be processed into food products to increase their added value. This research aims to obtain the process and product design of papaya jelly candy, as well as an overview of consumer acceptance of the resulting product. The cooking process is carried out at a temperature of 80°C for 5 minutes. The drying process is conducted at a temperature of 50°C for 24 hours, followed by additional drying at 70°C for 2 hours. The product design is achieved through the development of formulation based on the results of organoleptic test, quality testing, and product packaging design. The best formulation for the jelly candy is achieved with the ingredient composition of 1200 grams of calina papaya, 72 grams of jelly powder, 18 grams of pectin, 120 grams of water, 12 grams of collagen, 360 grams of granulated sugar, 12 grams of flavoring, 0,6 grams of coloring, 3,6 grams of citric acid, and 24 grams of powdered sugar. The product is packaged in plastic jar. The consumer acceptance results indicate sales feasibility and purchase intention for the jelly candy product approved by over 90% of the respondents.
Keyword: jelly candy, process design, product design, rejected papaya

Judul: Process and Product Design of Sukade Calina Papaya Rejected
Abstrak: Pepaya calina afkir yang ada di KN Jaya Farm berjumlah cukup besar dan saat ini dimanfaatkan untuk konsumsi sendiri dalam jumlah yang kecil atau dijual murah ke pasar. Salah satu kategori pepaya afkir yang ada adalah pepaya yang masih terlalu muda sehingga berpotensi untuk diolah menjadi produk pangan seperti sukade. Prosedur penelitian yang digunakan dalam desain proses dan produk meliputi tahap karakterisasi buah pepaya calina muda sebagai identifikasi awal bahan baku penelitian, tahap desain proses pengolahan produk sukade, tahap desain produk sukade yang mencakup formulasi produk, karakterisasi produk terpilih dan desain kemasan produk sukade, serta tahap terakhir yaitu pengujian penerimaan konsumen terhadap produk sukade terpilih yang sudah dirancang dalam penelitian. Hasil desain proses pengolahan sukade meliputi perbaikan dan penyesuaian proses pemotongan, pencucian, perendaman dalam larutan kapur sirih, pencucian kembali, pemblansiran, pemasakan, pewarnaan, perendaman dalam larutan gula dan pewarna selama 24 jam serta pengeringan pada suhu 70℃ selama 5 jam. Hasil desain produk meliputi formulasi terpilih dari produk sukade dengan komposisi pepaya calina muda, gula pasir, bubuk kapur sirih, asam sitrat, vanili bubuk, pewarna alami dari bahan dasar saffron, dan air yang digunakan untuk pemasakan dan perendaman sukade. Hasil uji karakteristik produk sukade mengikuti syarat mutu manisan buah kering dengan kadar air akhir produk sebesar 11,765%. Hasil penilaian dan penerimaan konsumen menyatakan 100% produk sukade sudah layak untuk dijual dengan minat beli konsumen sebesar 89,7%. Penelitian lanjutan yang perlu dilakukan adalah pengujian umur simpan dan peningkatan skala produksi., There are quite a large quantities of rejected calina papaya at KN Jaya Farm which are used for self-consumption or by sold cheaply to the market. One category of rejected papaya that exists is unripe papaya so it has the potential to be processed into food products such as sukade. The research procedures used in process and product design are the characterization stage of unripe calina papaya as the initial identification of research raw materials, the process design stage of the sukade product, the product design stage of sukade which includes the product formulation, the characterization of selected product and the packaging design of sukade product. The last stage is testing consumer acceptance of selected sukade product that have been designed in the research. The results of the process design stage include repair and modification process of cutting, washing, soaking in whiting solution, backwashing, blanching, cooking (boiling), coloring, soaking in sugar and color solution for 24 hours and the last is drying process with drying oven at 70℃ for 5 hours. The results of the sukade product design stage is the selected formulation include unripe calina papaya, granulated sugar, whiting powder, citric acid, vanilla powder, natural color made from saffron base, and water which are used for cooking and soaking sukade in sugar. The test results for the characteristics of sukade product followed the quality requirements for candied dried fruit with a final product moisture content of 11.765%. The results of the consumer evaluation and acceptance stated that 100% of sukade products were suitable for sale with a consumer buying interest of 89.7%. Suggested further research is testing the shelf life and increasing the production
Keyword: calina papaya, dried sweets, process design, processed product, sukade

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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