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- Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.A manager uses this equation to predict demand for landscaping services: Ft = 14 + 4t. Over the past eight periods, demand has been as follows: Period, t: 1 2 3 4 5 6 7 8 Demand: 20 25 25 35 35 40 45 50 Compute the tracking signals for Periods 1-8. (Negative values should be indicated by a minus sign. Round your intermediate calculations and final answers to 3 decimal places.) Period t Tracking Signal 1 2 3 4 5 6 7 8
- "A chipboard company has 4 factories, Mazatenango, Retalhuleu, Escuintla and Xela. It has four major distributors of its chipboards, which are distributor 1, distributor 2, distributor 3 and distributor 4: Mazatenango Retalhuleu Escuintla Xela DEMAND D1 10 16 19 12 350 D2 12 10 18 15 300 D3 15 22 10 10 250 IN THIS CASE USE VOGEL'S APPROXIMATION METHOD D4 20 10 12 20 200 SUPPLY 150 150 350 250 1) Formulate the problem as a transportation problem, solve it with the three methods and find the optimal cost for this problem. methods and find the optimal cost for this transportation problem. (remember to go through all possible routes).North Dakota Electric Company estimates its demand trend line (in millions of kilowatt hours) to be: D = 80.0 + 0.43Q, where Q refers to the sequential quarter number and Q = 1 for winter of Year 1. In addition, the multiplicative seasonal factors are as follows: Quarter Factor (Index) Winter 0.80 Spring 1.25 Summer 1.45 Fall 0.50 In year 26 (quarters 101-104), the energy use for each of the quarters beginning with winter is (round your response to one decimal place): Quarter Energy Use Winter 98.798.7 Spring nothingNorth Dakota Electric Company estimates its demand trend line (in millions of kilowatt hours) to be: D = 80.0 + 0.43Q, where Q refers to the sequential quarter number and Q = 1 for winter of Year 1. In addition, the multiplicative seasonal factors are as follows: Quarter Factor (Index) Winter 0.80 Spring 1.25 Summer 1.45 Fall 0.50 In year 26 (quarters 101-104), the energy use for each of the quarters beginning with winter is (round your response to one decimal place):
- North Dakota Electric Company estimates its demand trend line (in millions of kilowatt hours) to be: D = 80.0 + 0.50Q, where Q refers to the sequential quarter number and Q = 1 for winter of Year 1. In addition, the multiplicative seasonal factors are as follows: Quarter Factor (Index) Winter 0.80 Spring 1.25 Summer 1.50 Fall 0.45 In year 26 (quarters 101-104), the energy use for each of the quarters beginning with winter is (round your response to one decimal place): Quarter Energy Use Winter Spring Summer Fall2. Consider the transportation problem having the following parameter table (M is a big positive number) Source Demand 1 12345 2 3 5 1 2 3 343800 13 14 4 18 3 0 130940 Destination 4 5 22 29 18 21 M 3 5 26M940 16 M 11 24 34 19 23 11 4 6 Supply 0 ooooo 0 6 0 0 36 28 0 5 6 2 56743 (a) Use the northwest corner rule manually to obtain a complete initial BF solution, also find the objective value for this solution. How many basic variables are there in this solution? (b) Use Vogel's approximation method manually to select the first basic variable for an initial BF solution. (Attention, do not need to find an complete initial BF solution, just find the first BV for this initial BF solution)15) JBs needs to determine what quantity of a new tennis racquet to order for the upcoming summer season. They sell the racquet for $110 and procure it from their supplier for $70. Any leftovers will be marked down 60% and are expected to all sell at that price. Anticipated demand is modeled with a normal distribution where the mean is 120 and the standard deviation is 25. How many racquets should JBs order if they want to meet a 95% target fill rate? A) 130 C) 162 B) 127 D) 149
- North Dakota Electric Company estimates its demand trend line (in millions of kilowatt hours) to be: D = 77.0 +0.43Q, where Q refers to the sequential quarter number and Q = 1 for winter of Year 1. In addition, the multiplicative seasonal factors are as follows: Quarter Winter Spring Summer Fall In year 26 (quarters 101-104), the energy use for each of the quarters beginning with winter is (round your response to one decimal place): Quarter Winter Factor (Index) 0.80 1.20 1.40 0.60 Spring Summer Fall Energy UseAs a demand planner at Grootegeluk Mine, you want to determine the monthly sales forecast of coal (in tonnes). Table 1, below, depicts the volume of coal sold by the mine for each of the 12 months of 2022.Table 1: Volume of coal sold monthly during 2022 Year Monthly volume (tonne s) Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 2022 21 23 34 37 40 51 54 50 48 36 39 42 1. Using the three-month weighted moving average method, calculate the monthly forecasts for April 2022 to January 2023 by assigning weights of 0.1, 0.3, and 0.6 (the oldest data to the most recent data, respectively) (Round off forecast values to one decimal place). 2. Calculate the mean absolute deviation (MAD) of the forecasts for April 2022 to December 2022 (Round off the answer to two decimal place). 3.18. New car sales for a dealer in Cook County, Illinois, for the past year are shown in the following table, along with monthly indexes (seasonal relatives), which are supplied to the dealer by the regional distributor. Month Jan. Feb. Mar. Apr. May. Jun. Jul. Aug. Sept. Oct. Nov. Dec. Units Sold 640 648 630 761 735 850 765 805 840 828 840 800 Index 0.80 0.80 0.70 0.94 0.89 1.00 0.90 1.15 1.20 1.20 1.25 1.25 a. Plot the data. Does there seem to be a trend? b. Deseasonalize car sales. c. Plot the deseasonalized data on the same graph as the original data. Comment on the two graphs. d. Assuming no proactive approach on the part of management, discuss (no calculations neces- sary) how you would forecast sales for the first three months of the next year. e. What action might management consider based on your findings in part b?