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IML336 1213, HW -2 Problem 1 A company manufactures four variants of the same product and in the final part of the manufacturing process there are...

Julie's Diamond Boutique is very concerned with its order policies related to one-carat F-24 Copyright 2011 Pearson Education, Inc. diamond solitaires. Their current policy is to order 10 diamonds whenever their inventory reaches 6 diamonds (unless there is already an ordered delivery due). Currently there are 8 diamonds on hand. Orders are placed at the end of the month and take one month to arrive (e.g., if an order is placed at the end of month 1, it will be available at the beginning of month 3). The following distribution of monthly sales has been developed using historical sales. If Julie's does not have a diamond on hand, it will result in a lost sale. Use the following random numbers to determine the number of lost sales of one-carat solitaires at Julie's over 12 months. Monthly sales Probability 3 .20 4 .30 5 .20 6 .20 7 .10 Random numbers for sales: 10, 24, 03, 32, 23, 59, 95, 34, 34, 51, 08, 48

IML336 1213, HW -2 Problem 1 A company manufactures four variants of the same product and in the final part of the manufacturing process there are assembly, polishing and packing operations. For each variant the time required for these operations is shown below (in minutes) as is the profit per unit sold. Assembly Polish Pack Profit (£) Variant1 2 3 2 1.50 Variant2 4 2 3 2.50 Variant3 3 3 2 3.00 Variant4 7 4 5 4.50 a) Formulate the problem using LP and solve it using Simplex method for below condition: Given the current state of the labor force the company estimate that, each year, they have 100000 minutes of assembly time, 50000 minutes of polishing time and 60000 minutes of packing time available. How many of each variant should the company make per year and what is the associated profit? b) Solve the problem with a software and interprete the sensitivity analysis results .
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Problem 2 a) Aşağıdaki problem formüle ediniz b) Bir yazılım (Excel, POM vs.) kullanarak çözünüz. Çözüm sonuçlarını kısa bir paragrafla açıklayınız. Şu an tarih 1 Ocak ve MFG bisiklet imalatçısı şirketin önümüzdeki 4 dönemlik talep tahminini aşağıdaki gibi belirlemiş: Quarter Satış (adet) 1 5000 2 10000 3 8000 4 2000 1 Ocakta elde 1000 adet stok var. Maliyetler şu şekilde (TL): İşe alma:200 İşten çıkarma:400 Başlangıç iş gücü: 60 Stok masrafı : 2/parça/dönem (dönem sonu envanteri ile hesaplanacak) Stoksuz kalma masrafı: 50/adet Normal mesai maaşı: 1200/çalışan/dönem Fazla mesai masrafı: 2/adet (çalışan başına dönemde maksimum 40 olabiliyor) Her çalışan normal mesaide, dönem başına 100 adet üretebiliyor. Aynı dönemde karşılanmayan talep, kayıp satış olmakta. Problem 3 Aşağıdaki soruları Maximize: z=20x 1 +30x 2 +25x 3 probleminin Simplex metodu ile çözümü sırasında elde edilen aşağıdaki tabloya göre cevaplayınız. Basic z x 1 x 2 x 3 s 1 s 2 s 3 Sol’n Ratio z 1 85 0 0 25 -20 0 --- 0 3 0 1 1 -2 0 100 0 1 1 0 0 1 0 200 0 -5 0 0 -2 4 1 400 (a) Yukarıdaki Simplex tablosunu denklemler şeklinde yazınız. (b) Temel ve temel olmayan değişkenler hangileridir? (c) Bu çözüm anındaki değişken değerleri ve amaç fonksiyon değeri nedir? (d) Bu çözüm noktası optimum çözüm müdür? Değilse giren ve çıkan değişkenler hangileri olacaktır, ve optimum çözüm sonucu ne olacaktır?
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