Consider that the annual demand of a product is uniformly distributed between 200 and 300 units. Profit per unit sold is 10,000 rupees and the annual cost can be assumed to be constant at 23,00,000 rupees. Obtain distribution and density functions of random profit.
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Consider that the annual demand of a product is uniformly distributed between 200 and 300 units. Profit per unit sold is 10,000 rupees and the annual cost can be assumed to be constant at 23,00,000 rupees. Obtain distribution and density functions of random profit.
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- Barbara Flynn sells papers at a newspaper stand for $0.40. The papers cost her $0.30, giving her a $0.10 profit on each one she sells. From past experience Barbara knows that: a) 20% of the time she sells 150 papers. b) 20% of the time she sells 200 papers. c) 30% of the time she sells 250 papers. d) 30% of the time she sells 300 papers. Assuming that Barbara believes the cost of a lost sale to be $0.05 and any unsold papers cost her $0.30 and she orders 250 papers. Use the following random numbers: 14, 4, 13, 9, and 25 for simulating Barbara's profit. (Note: Assume the random number interval begins at 01 and ends at 00.) Based on the given probability distribution and the order size, for the given random number Barbara's sales and profit are (enter your responses for sales as integers and round all profit responses to two decimal places): Random Number Sales Profit 14 4 13 9 25The owner of a boat has estimated the following distribution of demand for a particular kind of boat. No. demanded o 1 2 3 Probability 0.10 0.20 0.30 0.40 Each boat costs him (c + d) rials and he sells them for (2 • c + 2 • d) rials each. Prices are given in hundreds rial units. Boats that are left unsold at the end of the season must be disposed off for (c + d – 2) rials each. How many should be stocked so as to maximize his expected profit?The weekly demand of a slow-moving product has the probability mass function shown to the right. Find the expected value, variance, and standard deviation of weekly demand. The expected value of weekly demand is 1 (Type an integer or a decimal. Do not round.) The variance of weekly demand is 6. (Type an integer or a decimal. Do not round.) The standard deviation of weekly demand is (Round to three decimal places as needed.) Demand, x Probability, f(x) 0.3 0.2 IT 0.4 0.1 0.0 4 or more
- A lathe costs $56,000 and is expected to result in net cash inflows of $20,000 at the end of each year for three years and then have a market value of $10,000 at the end of the third year. The equipment could be leased for $22,000 a year, with the first payment due immediately. If the organization does not pay income taxes and its MARR is 10%, show whether the organization should lease or purchase the equipment.A monopolist's total cost is TC = 4.5Q, where Q is output. Demand is Q = 10 - P , where P is price. When the monopolist chooses the profit maximizing Q*, the profit earned isA manufacturer has a production facility that requires 15,604 units of component JY21 per year. Following a long-term contract, the manufacturer purchases component JY21 from a supplier with a lead time of 7 days. The unit purchase cost is $25.6 per unit. The cost to place and process an order from the supplier is $121 per order. The unit inventory carrying cost per year is 10.5 percent of the unit purchase cost. The manufacturer operates 250 days a year. Assume EOQ model is appropriate. If the manufacturer uses a constant order quantity of 2,640 units per order, what is the annual holding cost? Use at least 4 decimal places.
- Consider a toy retailer with warehouses in St. Louis and Kansas City, Missouri. The warehouses stock an identical popular toy delivered to stores in the two cities. Assume a warehouse serves only stores in its city. Weekly demand for St. Louis is normally distributed with mean 2,000, and standard deviation 400 (that is N(μ = 2,000, σ = 400)). Weekly demand for KansasCity is distributed N(μ = 2,000, σ = 300). We assume that the two cities are far enough apart so that demand in the two cities is independent.The following parameters are seen by both warehouses:Replenishment lead time in weeks ~ N(μ = 2, σ = 0.1);Fixed shipping cost of replenishment: $500;Cost per toy: $10; andHolding cost per toy 20 percent of toy’s value per year.How many toys should each location order at a time and when should they reorder if they want a 99 percent cycle service level? What if they pool the two locations?Your County has asked you to analyze the purchase of some dump trucks. Each truck wil cost $45,000 and have an operating and maintaining cost that starts at $15,000 the first year and increases by $ 2,000 per year. Assume the salvage value at the end of year is $9,000 and the interest rate is 12%. Estimate the equivalent annual cost of each truck.Why distribution range negative infinity to positive infinity is transformed to zero to positive infinity? ( probability distribution)
- I need a detailed explanation on how to solve this problem: A bagel shop buys each bagel for $0.08 and sells each bagel for $0.35. Leftover bagels at the end of the day are purchased by a local soup kitchen for $0.03 per bagel. The shop’s owner has observed for the daily demand, Q, the following probabilities, f(Q): Q 0 5 10 15 20 25 30 35 f(Q) 0.05 0.10 0.10 0.20 0.25 0.15 0.10 0.05 - What is the optimal daily order in multiples of 5 (include the model name and formula)? - If the daily demand is normally distributed (the mean and variance can be obtained from the table above), then what is the optimal daily order?Your answer is partially correct. An independent contractor for a transportation company needs to determine whether she should upgrade the vehicle she currently owns or trade her vehicle in to lease a new vehicle. If she keeps her vehicle, she will need to invest in immediate upgrades that cost $5,200 and it will cost $1,300 per year to operate at the end of year that follows. She will keep the vehicle for 5 years; at the end of this period, the upgraded vehicle will have a salvage value of $3,800. Alternatively, she could trade in her vehicle to lease a new vehicle. She estimates that her current vehicle has a trade-in value of $9,800 and that there will be $4,100 due at lease signing. She further estimates that it will cost $2,900 per year to lease and operate the vehicle. The independent contractor's MARR is 11%. Compute the EUAC of both the upgrade and lease alternatives using the insider perspective. Click here to access the TVM Factor Table Calculator. 1943.56 EUAC(keep): $…Consider a two-tier supply chain with one manufacturer and one retailer whointeract in a single selling season. The manufacturer sells a product to the retailer, who in turn sells in the market. Demand E is uncertain with cumulative distribution function F (·)and probability density function f (·). Since the production lead time is much longer thanthe selling season, the retailer must place a single order before demand is realized and cannotreplenish her inventory during the season. The retailer sells the product at an exogenousand fixed retail price r. The manufacturer produces the product at a unit cost of c. Themanufacturer uses a linear sales rebate contract and determines the following contract terms:For each unit ordered, he charges the retailer a wholesale price w, and for each unit sold, hepays the retailer a rebate s. Assume that the product has zero salvage value at the end ofthe season, and the inventory holding cost during the season is…