DEPARTMENT OF APPLIED MATHEMATICS BSc Honours in Businesses Research and Applied Statistics SMO 1101 Introduction to Businesses Research TUTORIAL QUESTIONS 1 . List and discuss the six significant steps in the quantitative modeling process. installment payments on your What is the difference between a i. detailed and a normative model? ii. under the radar and a continuous variable? three or more. Show the set в„њ n is a convex established. 4. Is a linearity presumption, in LP models, genuine in applications? 5. Print-Rite assembles machines for personal computer systems. These computer printers are set up at five different points along the development line. Each production series consists of five work clubs with different amounts of skill. Each team can be assigned to the of the five assembly details. The following desk gives the time, in minutes, to accomplish the tasks at each assembly point for the individual teams. Assembly 2 26 24 26 24 dua puluh enam Point three or more 40 35 28 thirty six 30 four 30 thirty-two 36 35 40 your five 26 18 18 twenty 24
Staff A B C G E
1 20 twenty two 24 twenty 20
Come up with a linear programming unit that will lessen the total set up time for a printer. 6. How come implementation a horrible aspect of the quantitative modeling process?
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six. A postal office shooting requires different numbers of full-time employees about different days of the week. The number of a lot of the time employees needed on each working day is given inside the table listed below. Employee Requirements for Post Office Day one particular = Monday Day a couple of = Tues Day 3 = Wed Day four = Thursday night Day your five = Thursday Day six = Weekend Day 7 = On the Number of A lot of the time Employees Needed 17 13 15 19 14 sixteen 11
Union rules claim that each full-time employee need to work five consecutive days and then acquire two days away. The mailbox wants to meet its daily requirements only using fulltime staff. Formulate a great LP model to minimize the number of full-time employees that must be chosen. 8. The Suny Organization, a company of VCRs (video cassette recorders), wants to plan the production and inventory amounts for the next six months. Its demand forecasts for six months are given in the second column from the table listed below: Unit Production Cost $460 $470 $480 $500 $500 $490 Maximum Production Level 7000 5000 4000 eight thousand 6000 3 thousands Minimum Production Level 3500 2500 2150 4000 3 thousands 1500 Maximum Inventory Level 7000 7000 7000 7000 7000 7000 Minimum Inventory Level 2500 2500 2300 2500 2300 2500
Month 1 2 3 5 5 6th
Demand Prediction 1000 4,000 6000 5000 3000 2k
Suny needs a plan that satisfies this kind of demand with no backlogging; that is certainly all require must be achieved in the month it happens. Owing to fluctuations in the costs of specific things like raw materials and utilities, a VCR's unit cost will be different from month to month. Another column in the table previously mentioned specifies Suny's forecasts of each month's product production costs. Suny's optimum production level also changes from month to month, due to such things as variations in each month's required routine service and the range of working days. It truly is Suny's coverage not to change its staff size from month to month. Consequently to avoid excessive negligence, Suny offers set the minimum month to month production level at 50% of the optimum monthly creation level. The table above's fourth and fifth articles contain each month's optimum and lowest production levels, respectively. Suny currently provides 3500 VCRs in products on hand. To ensure adequate safety stock, Suny offers
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specified 2300 VCRs since the minimum permissible inventory level at the conclusion of virtually any month. Provided the readily available storage space, Suny's maximum allowable inventory level at the end of any month is seven hundred VCRs. The table above's sixth and seventh columns contain every month's optimum and minimal inventory levels respectively. Suny's accounting section has approximated that it costs $8 per month to hold a VCR in inventory, including the opportunity cost of foregone fascination. Furthermore the accounting department recommends that Suny figure out each month's...
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