A company must meet the following demands (but backlogs and inventory allowed with charges) January 30; February 30; March 20 all demand must be met by end of March. Inventory costs $20/ unit at month end, and backlogged demand incurs a $5 / unit per month cost. This table lists the monthly production capacity and unit production costs. Month January February March Production Cap 35 30 35 Unit costs 400 420 410 Set up the transportation simplex (and then solve) where the rows are Monthly Supply and the Columns are the monthly deliveries. You'll need a dummy demander. A unit shipped from February Supply to a January demand is LATE. A unit shipped from a February Supply to a March demand has been put in Inventory for a month. 1. How many February units are shipped to February demand 2. What is the total optimal cost.
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- A Las Vegas supermarket bakery must decide how many wedding cakes to prepare for the upcoming weekend. Cakes cost $33 each to make, and they sell for $60 each. Unsold cakes are reducedto half-price on Monday, and typically one-third of those are sold. Any that remain are donated toa nearby senior center. Analysis of recent demand resulted in the following table:Demand 0 1 2 3Probability .15 .35 .30 .20How many cakes should be prepared to maximize expected profit?a. Use the ratio method.b. Use the tabular methodProblem 20-10 (Algo) You are a newsvendor selling San Pedro Times every morning. Before you get to work, you go to the printer and buy the day's paper for $0.30 a copy. You sell a copy of San Pedro Times for $1.10. Daily demand is distributed normally with mean = 265 and standard deviation = 53. At the end of each morning, any leftover copies are worthless and they go to a recycle bin. a. How many copies of San Pedro Times should you buy each morning? (Use Excel's NORMSINV() function to find the correct critical value for the given a-level. Round your z-value to 2 decimal places and final answer to to 2 decimal places.) Optimal order quantity b. Based on a, what is the probability that you will run out of stock? (Round your answer to the nearest whole number.) ProbabilityDemand for stereo headphones and music players for joggers has caused Nina Industries to grow almost 50 percent over the past year. The number of joggers continues to expand, so Nina expects demand for headsets to also expand, because, as yet, no safety laws have been passed to prevent joggers from wearing them. Demand for the players for this year was as follows: MONTH DEMAND (UNITS) January 4,150 February 4,250 March 3,950 April 4,350 May 4,950 June 4,650 July 5,250 August 4,850 September 5,350 October 5,650 November 6,250 December 5,950 a. Using linear regression analysis, what would you estimate demand to be for each month next year? Using a spreadsheet, follow the general format in Exhibit 3.8. (Do not round intermediate calculations. Round your answers to 2 decimal places.) b. To be reasonably confident of meeting demand, Nina decides to use 3 standard errors of estimate for safety. How many additional units should be held to meet this…
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- John buys goat milk at a cost of $5 per gallon from a local dairy and sells it for $8 per gallon in its store. The dairy will buy back any milk that is unsold at the end of the day for $2 per gallon. Each day John must determine how many gallons to order. Past sales have ranged between 15 and 18 gallons per day, according to the following demand pattern.Demand:15161718Number of days demand occurred:2486Assume that demand will be within this range in future.(a) What are the possible actions and states?(b) Determine the daily profit (rewards) and show on a reward table.(c) Using each of the following criteria, determine John’s best action.- Maximin- Maximax- Expected value(d) Construct the regret (opportunity cost) matrix and using minimax regret criteria determine John’s best action.A manager receives a forecast for next year. Demand is projected to be 600 units for the first half of the year and 920 units for the second half. The monthly holding cost is $2 per unit, and it costs an estimated $55 to process an order. a.Assuming that monthly demand will be level during each of the six-month periods covered by the forecast (e.g., 100 per month for each of the first six months), determine an order size that will minimize the sum of ordering and carrying costs for each of the six-month periods. (Round your answers to the nearest whole number.) Period Order Size 1 – 6 months?_____units 7 – 12 months?_____units b.If the vendor is willing to offer a discount of $10 per order for ordering in multiples of 50 units (e.g., 50, 100, 150), would you advise the manager to take advantage of the offer in either period? If so, what order size would you recommend? (Round intermediate calculations to 2 decimal places.) Period Order Size 1 – 6 months?____ units 7 – 12 months?____…. Worldwide Can-Openers, Inc., makes a family of two hand-operated can openers. The production plan is based on months. There are 4 weeks in this month. Opening inventory is 2000 dozen, and it is planned to increase that to 4000 dozen by the end of the month. The MPS is made using weekly periods. The forecast and projected available balance for the two models follow. The lot size for both models is 1000 dozen. Calculate the production plan and the MPS for each item.