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 Fruit Leather from Rejected Calina Papaya
Abstrak: Pepaya afkir merupakan kategori buah yang kualitasnya tidak memenuhi standar yang sudah ditentukan. Tujuan proyek ini mendapatkan desain proses dan produk olahan pepaya afkir yang dapat diaplikasikan pada skala kecil di KN Jaya Farm dan sesuai dengan minat Masyarakat. Tahapan proyek ini yaitu fase eksplorasi, pendefinisian masalah, ideasi, pengembangan prototipe, dan validasi. Observasi lapang dan wawancara dilakukan dengan mitra KN Jaya Farm. Permasalahan yang diketahui yaitu banyaknya pepaya afkir yang belum termanfaatkan. Ide solusi dari permasalahan yaitu diperlukan usaha diversifikasi produk olahan dari Pepaya Calina, yaitu fruit leather. Pengembangan prototipe dilakukan dengan desain proses pemasakan dan pengeringan. Pemasakan dilakukan pada suhu 80oC selama 3 sampai 5 menit dan pengeringan dilakukan pada suhu 50oC selama 18 jam. Formula terbaik untuk fruit leather yaitu Pepaya Calina (500 gram), mangga (250 gram), gula pasir (112,5 gram), air (30 gram), icing sugar (20 gram), pektin (7,5 gram), kulit jeruk nipis (2,5 gram), dan asam sitrat (1,5 gram), dengan rendemen sebesar 25,11%. Hasil organoleptik menghasilkan nilai rata-rata disukai berdasarkan parameter warna, aroma, rasa, dan tekstur. Desain produk dilakukan dengan memilih kemasan toples plastik Polyethylene Terephthalate (PET) serta label. uji penerimaan target konsumen terhadap produk menyatakan bahwa 93,7% responden menyatakan produk layak untuk dijual dan 85,7% responden berminat untuk membeli produk fruit leather., Rejected papaya is a category of fruit whose quality does not meet predetermined standards. The aim of this project is to obtain a process design and processed product of rejected papaya that can be applied on a small scale at KN Jaya Farm and in accordance with the interests of the community. The stages of this project are the exploration phase, problem definition, ideation, prototype development, and validation. Field observations and interviews were conducted with KN Jaya Farm partners. The known problem is the large number of rejected papayas that have not been utilized. The idea of a solution to the problem is that it is necessary to diversify processed products from Calina Papaya, namely fruit leather. Prototype development is done by designing the cooking and drying process. Cooking is done at 80oC for 3 to 5 minutes and drying is done at 50oC for 18 hours. The best formula for fruit leather is papaya calina (500 grams), mango (250 grams), sugar (112.5 grams), water (30 grams), icing sugar (20 grams), pectin (7.5 grams), skin lime (2.5 grams), and citric acid (1.5 grams), with a yield of 25.11%. The organoleptic results yielded the preferred average values based on the parameters of color, aroma, taste and texture. Product design is done by choosing Polyethylene Terephthalate (PET) plastic jar packaging and labels. test of consumer acceptance of the product stated that 93.7% of respondents said the product was fit for sale and 85.7% of respondents were interested in buying fruit leather products.
Keyword: product diversification, formulation, fruit leather, calina papaya, validation

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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