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 400 250 $2,400 $2,400 $2,400 $2,400 $900 $3,900 $3,900 $3,300 500 ($100) $2,900 $4,900 $3,400
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- Sometimes curvature in a scatterplot can be fit adequately (especially to the naked eye) by several trend lines. We discussed the exponential trend line, and the power trend line is discussed in the previous problem. Still another fairly simple trend line is the parabola, a polynomial of order 2 (also called a quadratic). For the demand-price data in the file P13_10.xlsx, fit all three of these types of trend lines to the data, and calculate the MAPE for each. Which provides the best fit? (Hint: Note that a polynomial of order 2 is still another of Excels Trend line options.)13 Pam’s demand for hats is normally distributed with mean 500 and standard deviation 100. She sells her hats for $50 each and buys hats for $10 each, and anything she can't sell by the end of the year, the wholesaler will buy for $5 each. How many hats should she order for next year to maximize profit?3. Cynthia Knott’s oyster bar buys fresh Louisiana oysters for $5 per pound and sells them for $12 per pound. Any oysters not sold that day are sold to her cousin, who has a nearby grocery store, for $1 per pound. Cynthia believes that demand follows the normal distribution, with a mean of 100 pounds and a standard deviation of 15 pounds. a) What is the cost of underestimating demand for each pound? b) What is the overage cost per pound? c) How many pounds of oyster should she order each day? d) What is the stockout risk for this order size?
- 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?Cynthia Knott's oyster bar buys fresh Louisiana oystersfor $5 per pound and sells them for $9 per pound. Any oysters notsold that day are sold to her cousin, who has a nearby grocery store,for $2 per pound. Cynthia believes that demand fo llows the normaldistribution, with a mean of I 00 pounds and a standard deviation of15 pounds. How many pounds should she order each day?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?
- Annual demand for number 2 pencils at the campus store is normallydistributed with mean 1,000 and standard deviation 250. The store purchases thepencils for 6 cents each and sells them for 20 cents each. There is a two-monthlead time from the initiation to the receipt of an order. The store accountantestimates that the cost in employee time for performing the necessary paperworkto initiate and receive an order is $20, and recommends a 22 percent annual interest rate for determining holding cost. The cost of a stock-out is the cost of lostprofit plus an additional 20 cents per pencil, which represents the cost of loss ofgoodwill.b. Find the simultaneous optimal values of Q and R.Annual demand for number 2 pencils at the campus store is normallydistributed with mean 1,000 and standard deviation 250. The store purchases thepencils for 6 cents each and sells them for 20 cents each. There is a two-monthlead time from the initiation to the receipt of an order. The store accountantestimates that the cost in employee time for performing the necessary paperworkto initiate and receive an order is $20, and recommends a 22 percent annual interest rate for determining holding cost. The cost of a stock-out is the cost of lostprofit plus an additional 20 cents per pencil, which represents the cost of loss ofgoodwill.d. What is the safety stock for this item at the optimal solution?A distributor of large appliances needs to determine the order quantities and reorderpoints for the various products it carries. The following data refer to a specii c refrigeratorin its product line:Cost to place an orderHolding costCost of refrigeratorAnnual demandStandard deviation of demand during lead timeLead time$10020 percent of product cost per year$500 each500 refrigerators10 refrigerators7 daysConsider an even daily demand and a 365-day year.a. What is the economic order quantity?b. If the distributor wants a 97 percent service probability, what reorder point, R, shouldbe used?
- Annual demand for number 2 pencils at the campus store is normallydistributed with mean 1,000 and standard deviation 250. The store purchases the pencils for 6 cents each and sells them for 20 cents each. There is a two-month lead time from the initiation to the receipt of an order. The store accountant estimates that the cost in employee time for performing the necessary paperwork to initiate and receive an order is $20, and recommends a 22 percent annual interest rate for determining holding cost. The cost of a stock-out is the cost of lost profit plus an additional 20 cents per pencil, which represents the cost of loss of goodwill.a. Find the optimal value of the reorder point R assuming that the lot size used is the EOQ.b. Find the simultaneous optimal values of Q and R.c. Compare the average annual holding, setup, and stock-out costs of the policies determined in parts (a) and (b).d. What is the safety stock for this item at the optimal solution?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?MT makes small camping and snowmobile trailers. The demand for camping trailers occurs between January and June (mostly in April and May). MT makes camping trailers from January to June, shuts down in July and then makes snowmobile trailers from August to November. Suppose now is the end of December. For simplicity, we consider every two months as a period. The forecasts for camping trailers during each of the next three periods (six months) are: Period 1: 869 period 2: 1730 Period 3: 1374 MT employs 40 permanent workers who are paid an average of $20 per hour (including fringe benefits) and work approximately 320 hours a period (2 months). They make approximately 1,000 camping trailers per period during regular time. They can also work up to 50 percent more as overtime (i.e., up to 12 hours a day vs. the regular 8 hours a day) and will be paid 1.5 times the regular wage rate. Alternatively, MT can hire up to 40 additional temporary workers to work during a second shift. Hiring cost is…