during the months of October November and December 10000 kg during the months

During the months of october november and december

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during the months of October, November and December; 10,000 kg during the months of January, February, March and April; and 30,000 kg during the remaining months. The demand of product 2 is 50,000 kg during the months of October through February and 15,000 kg during the remaining months. Suppose that cost of producing a kg of product 1 and 2 is $5 and $8, respectively, provided that these were produced prior to June. After June, the costs are reduced to $4.5/kg and $7/kg because of the installation of an improved production system. The total amount of products 1 and 2 that can be produced during any particular month cannot exceed 120,000 kg for Jan-Sept and 150,000 kg for Oct-Dec. Furthermore, at the end of each month products left at the hand are carried to the inventory space in order to be used in the coming months. Each kg of product 1 occupies 2 cubic-feet and each kg of product 2 4 cubic-feet of inventory. Suppose that the maximum inventory space allocated to these products is 150,000 cubic-feet and that the holding cost per cubic foot during any month is $0.10. Formulate the production scheduling problem so that total production and inventory costs are minimized. Q3) A paper manufacturer produces rolls of standard fixed width w and of standard length l . Customers order rolls of width w but varying lengths. In particular, d k rolls with length l k and width w are ordered for customer k =1…n (assume l k ≤ l forall k=1. ..n ). What is the minimum number of rolls that should be cut to meet the demand? Hint: Let M be a large number such that M number of rolls are enough to satisfy all demand (e.g. M= ? 𝑘 𝑛 𝑘=1 ). Assume the manufacturer has M number of unmanufactured rolls in the stock. Use the following decision variables: ? 𝑖 = { 1 𝑖? ???? 𝑖 𝑖? ???? 0 ?. ?. 𝑖 = 1 … 𝑀 ? 𝑖𝑘 = ?????? ?? ????? ?? ???? ? (?? ?????ℎ ? 𝑘 )??? ???? ???? 𝑖, 𝑖 = 1 … 𝑀, ? = 1 … ? Q4) A power plant has three boilers. If a given boiler is operated, it can be used to produce a quantity of steam (in tons) between the minimum and maximum given in the first table below. The cost of producing a ton of steam on each boiler is also given. Steam from the boilers is used to produce power on three turbines. If operated, each turbine can process an amount of steam (in tons) between the minimum and maximum given in the second table. The cost of processing
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