Hi please answer this question fully 3. A pastry shop is considering how much hot chocolate to prepare each morning. Hot chocolatecosts $0.20 per oz to make and sells for $0.90 per oz. Customers can buy hot chocolate in anynumber of ounces that they wish. Any hot chocolate not sold by the end of the day is discarded.The daily demand for hot chocolate is normally distributed with a mean of 1,000 oz and a standarddeviation of 200 oz. How much hot chocolate should the pastry shop make each morning? Youmay use a z-table for this question.

To solve this problem, we need to determine the optimal amount of hot chocolate to prepare each…

Answered: 3. A pastry shop is considering how…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter3: Introduction To Optimization Modeling

Section3.8: A Multiperiod Production Model

Problem 22P

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Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.
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?
3. A pastry shop is considering how much hot chocolate to prepare each morning. Hot chocolate costs $0.10 per oz to make and sells for $0.40 per oz. Customers can buy hot chocolate in any number of ounces that they wish. Any hot chocolate not sold by the end of the day is discarded. The daily demand for hot chocolate is normally distributed with a mean of 1,200 oz and a standard deviation of 150 oz. How much hot chocolate should the pastry shop make each morning? You may use a z-table for this question.
A local outdoor vegetable stand has exactly 1,000 square feet of space to displaythree vegetables: tomatoes, lettuce, and zucchini. The appropriate data for theseitems are given in the following table.ItemTomatoes Lettuce ZucchiniAnnual demand 850 1,280 630(in pounds)Cost per pound $0.29 $0.45 $0.25The setup cost for replenishment of the vegetables is $100 in each case, and thespace consumed by each vegetable is proportional to its costs, with tomatoes requiring 0.5 square foot per pound. The annual interest rate used for computingholding costs is 25 percent. What are the optimal quantities that should be purchased of these three vegetables?
Dorothy’s pastries are freshly baked and sold at several spe-cialty shops throughout Perth. When they are a day old, theymust be sold at reduced prices. Daily demand is distributedas follows:Demand Probability50 0.25150 0.50200 0.25Each pastry sells for $1.00 and costs $0.60 to make. Each onenot sold at the end of the day can be sold the next day for$0.30 as day-old merchandise. How many pastries should bebaked each day?
Forrest and Dan make boxes of chocolates for which the demand is uncertain. Forrest says, “That’s life.” On the other hand, Dan believes that some demand patterns exist that could be useful for planning the purchase of sugar, chocolate, and shrimp. Forrest insists on placing a surprise chocolatecovered shrimp in some boxes so that “You never know what you’ll get.” Quarterly demand (in boxes of chocolates) for the last 3 years follows: Quarter Year 1 Year 2 Year 3 1 2 3 4 3,000 1,700 900 4,400 3,300 2,100 1,500 5,100 3,502 2,448 1,768 5,882 Total 10,000 12,000 13,600 a. Use intuition and judgment to estimate quarterly demand for the fourth year.b. If the expected sales for chocolates are 14,800 cases for year 4, use the multiplicative seasonal method to prepare a forecast for each quarter of the year. Are any of the quarterly forecasts different from what you thought you would get in part (a)?
A department store uses a (Q, R) policy to control its inventories. Sales of a pocket FM radioaverage 1.4 radios per week. The radio costs the store $50.00, and fixed costs of replenishmentamount to $20.00. Holding costs are based on a 20 percent annual interest charge, and thestore manager estimates a $12.50 cost of lost profit and loss of goodwill if the radio is demanded when out of stock. Reorder lead time is 2 weeks, and statistical studies have shownthat demand over the lead time is accurately described by a Poisson distribution. Find the optimallot sizes and reorder points for this item.
Henrique Correa's bakery prepares all its cakesbetween 4 A.M. and 6 A.M. so they will be fresh when customersarrive. Day-old cakes are virtually always sold, but at a 50% discountofT the regular $ 10 price. The cost of baking a cake is $6, anddemand is estimated to be normally distributed, with a mean of25and a standard deviation of 4. What is the optimal stocking level?
A supermarket in Seattle must decide how many wedding cakes to prepare for the upcomingweekend. Cakes cost $33 each to make, and they sell for $60 each. At the very last hour of theday, any unsold boxes are reduced to “half-price”. Holding cost is negligible. Analysis of recentdemand resulted in the following table: Demand Probability 0 .15 1 .35 2 .30 3 .20 How many cakes should be prepared to maximize expected profit?
Exercise 2: The demand per year (D) for product X is 12,100 units. The costs of placing an order (S) are $4.50. The unit cost (C) of the item is $25.00. The maintenance cost (H) per unit per year is 30% of the item's cost. 1. Use the economic order quantity (EOQ) model to determine: *Optimal quantity to order* The expected number of orders*Optimal time between orders*The total annual cost of maintaining that optimal amountNOTE: Show calculations of how you arrived at each amount 2. Answer, what are the potential benefits of using EOQ analysis for inventory management? How can you help businesses strike a balance between inventory holding costs and ordering costs?
H&M’s chief demand planner has estimated that 9,250,000 units of clothing will be sold in 2021. H&M’scost of placing and processing an order is R250, while the annual cost of holding a unit in its distributioncentre is projected at 5% of the unit purchase price. Both costs are expected to be constant for theforeseeable future. On average H&M sells a unit of clothing for R300.00 at cost plus 50%. Orders arereceived two weeks after being placed with the supplier. Assume a 365-day year and that demand isconstant throughout the year.Furthermore, as part of the drive towards operational efficiency, the chief demand planner is thinkingabout using the seasonally-adjusted moving average method to forecast demand for H&M’s clothingfor the 2021 financial year. In this regard, Mrs Masuku has retrieved from the retailer’s database thefollowing information on number of clothing sold over a four–year period.Year Quarterly sales (‘000 units)Q1 Q2 Q3 Q42016 1300 1500 1200 20002017 1600…
A newspaper publisher uses roughly 800 feet of baling wire each day to secure bundles of newspapers while they are being distributed to carriers. The paper is published Monday through Saturday.Lead time is six workdays. What is the appropriate reorder point quantity, given that the companydesires a service level of 95 percent, if that stockout risk for various levels of safety stock is as follows: 1,500 feet, .10; 1,800 feet, .05; 2,100 feet, .02; and 2,400 feet, .01?

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