Jim's Camera shop sells two high-end cameras, the Sky Eagle and Horizon. The demands and selling prices for these two cameras are as follows. Ds = demand for the Sky Eagle Ps = selling price of the Sky Eagle DH demand for the Horizon PH selling price of the Horizon = Ds = 226 -0.60PS + 0.35PH DH = 265 +0.10Ps - 0.64Pp H The store wishes to determine the selling price that maximizes revenue for these two products. Develop the revenue function R (in terms of P and P only) for these two models, and find the prices (in dollars) s PH that maximizes revenue. (Round your answers to two decimal places.) Revenue R = Price for Sky Eagle P = $ S Price for Horizon PH = $ Optimal revenue R = $
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- Use @RISK to analyze the sweatshirt situation in Problem 14 of the previous section. Do this for the discrete distributions given in the problem. Then do it for normal distributions. For the normal case, assume that the regular demand is normally distributed with mean 9800 and standard deviation 1300 and that the demand at the reduced price is normally distributed with mean 3800 and standard deviation 1400.Dilberts Department Store is trying to determine how many Hanson T-shirts to order. Currently the shirts are sold for 21, but at later dates the shirts will be offered at a 10% discount, then a 20% discount, then a 40% discount, then a 50% discount, and finally a 60% discount. Demand at the full price of 21 is believed to be normally distributed with mean 1800 and standard deviation 360. Demand at various discounts is assumed to be a multiple of full-price demand. These multiples, for discounts of 10%, 20%, 40%, 50%, and 60% are, respectively, 0.4, 0.7, 1.1, 2, and 50. For example, if full-price demand is 2500, then at a 10% discount customers would be willing to buy 1000 T-shirts. The unit cost of purchasing T-shirts depends on the number of T-shirts ordered, as shown in the file P10_36.xlsx. Use simulation to determine how many T-shirts the company should order. Model the problem so that the company first orders some quantity of T-shirts, then discounts deeper and deeper, as necessary, to sell all of the shirts.3. Gursoy is selling Christmas trees. She purchases trees for $10 and sells for $25 each. The number of trees she can sell is normally distributed with a mean of 100 and standard deviation of 30. How many trees should Gursoy purchase?
- A manufacturer of industrial sales has production capacity of 1,000 units per day. Currently, the firm sells production capacity for $10 per unit. At this price, all production capacity gets booked about one week in advance. A group of customers have said that they would be willing to pay $15 per unit if capacity was available on the last day. About ten days in advance, demand for the high-price segment is normally distributed with a mean of 250 and a standard deviation of 100. How much production capacity should the manufacturer reserve for the last day? Show the answer clearly.Topgun Records and several movie studios have decided to sign a revenue-sharing contract for CDs. Each CD costs the studio $2 to produce. The CD will be sold to Topgun for $3. Topgun, in turn, prices a CD at $15 and forecasts demand to be normally distributed, with a mean of 5,000 and a standard deviation of 2,000. Any unsold CDs are discounted to $1, and all sell at this price. Topgun will share 35 percent of the revenue with the studio, keeping 65 percent for itself. How many CDs should Topgun order? How many CDs does Topgun expect to sell at a discount? What is the profit that Topgun expects to make? What is the profit that the studio expects to make? Repeat parts (a)–(d) if the studio sells the CD for $2 (instead of $3) but gets 43 percent of revenue.A book and paper store distributes one specialized monthly magazine. When looking at the sales the last years, they have concluded that the demand for each issue of the magazine will be normally distributed with an expected sale of 250 and a standard deviation of 100. The purchase price for the magazine is $20. and the sales price is $50.The store has an agreement with a second -hand store that buys unsold magazines for $5 each. How many magazines should the store buy of each issue?
- Dan’s Independent Book Store is trying to decide on how many copies of a book to purchase at the start of the upcoming selling season. The book retails for $28.00. The publisher sells the book to Dan at $20.00. Dan can dispose of all of the unsold copies of the book at 50% off the retail price, at the end of the season. Dan estimates that demand for this book during the season is Normal with a mean of 1000 and a standard deviation of 250. Question 1: What is the quantity that Dan should order to maximize his expected profit?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) 149Barbara 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 25
- Irwin’s sells a particular model of fan, with most of the sales being made in thesummer months. Irwin’s makes a one-time purchase of the fans prior to eachsummer season at a cost of $40 each and sells each fan for $60. Any fans unsoldat the end of the summer season are marked down to $29 and sold in a special fallsale. Virtually all marked-down fans are sold. The following is the number of salesof fans during the past 10 summers: 30, 50, 30, 60, 10, 40, 30, 30, 20, 40.a. Estimate the mean and the variance of the demand for fans each summer.b. Assume that the demand for fans each summer follows a normal distribution,with mean and variance given by what you obtained in part (a). Determine theoptimal number of fans for Irwin’s to buy prior to each summer season.c. Based on the observed 10 values of the prior demand, construct an empiricalprobability distribution of summer demand and determine the optimal numberof fans for Irwin’s to buy based on the empirical distribution.d. Based on your…A company needs to order raw material and demand is forecast to be normally distributed with a mean of 250 gallons and standard deviation of 100 gallons. One gallon of raw material produces one gallon of product and the product sells for $25/gallon. Raw material costs $10/gallon but the company must also spend $5/gallon for disposal of any UNUSED raw material. If demand is higher than production capacity, the company sells what it can make and loses the rest of demand. a) If they buy 400 gallons of raw material, how much should they expect to spend on disposal costs (in $)? b) To have a 92% probability of satisfying demand, how many gallons of raw material should be bought?Flora Co sells bunches of fresh flowers which have a limited shelf life so forecasting sales demand is extremely important for maximising profits. Quarter 1 Quarter 1 contains a national holiday and as a result sales of a particular red flower are usually very high. Sales of the red flower will depend on market conditions. After the national holiday there will be no demand for the red flowers and they will be thrown away. Flora Co must decide whether to purchase 250 bunches, 400 bunches or 500 bunches of the red flowers from its supplier for re-sale to its customers. The following payoff table has been produced: Market conditions Poor Good Excellent Expected value Probability 0.20 0.25 0.55 Number of bunches to be bought from supplier 400 $900 $3,900 $3,900 250 $2,400 $2,400 $2,400 $2,400 $3,300 500 ($100) $2,900 $4,900 $3,400