Based on 3.10 problem 3: James Beerd bakes cheese cakes and Black Forest cakes. During any month he can bake at most 65 cakes. The cost per cake and the demands for cake, which must be met on time, are listed in the Table. It costs $ 1.50 to hold a cheesecake, and $ 1.20 to hold a Black Forest cake, in inventory for a month. Set up the LP and then determine the minimum cost to meet the demand. Month1 Month1 Month2 Month2 Month3 Month3 TYPE Demand Cost/cake Demand Cost/cake Demand Cost/cake cheesecake 41 9 30 10.2 20 11.4 BlackForest 20 7.5 30 8.4 10 10.2 The minimum cost subject to the conditions is

Based on 3.10 problem 3: James Beerd bakes cheese cakes and Black Forest cakes. During any month he can bake at most 65 cakes. The cost per cake and the demands for cake, which must be met on time, are listed in the Table. It costs $ 1.50 to hold a cheesecake, and $ 1.20 to hold a Black Forest cake, in inventory for a month. Set up the LP and then determine the minimum cost to meet the demand. Month1 Month1 Month2 Month2 Month3 Month3 TYPE Demand Cost/cake Demand Cost/cake Demand Cost/cake cheesecake 41 9 30 10.2 20 11.4 BlackForest 20 7.5 30 8.4 10 10.2 The minimum cost subject to the conditions is

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section: Chapter Questions

Problem 67P

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The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. As indicated by the algebraic formulation of the Pigskin model, there is no real need to calculate inventory on hand after production and constrain it to be greater than or equal to demand. An alternative is to calculate ending inventory directly and constrain it to be nonnegative. Modify the current spreadsheet model to do this. (Delete rows 16 and 17, and calculate ending inventory appropriately. Then add an explicit non-negativity constraint on ending inventory.)
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Modify the Pigskin model so that there are eight months in the planning horizon. You can make up reasonable values for any extra required data. Dont forget to modify range names. Then modify the model again so that there are only four months in the planning horizon. Do either of these modifications change the optima] production quantity in month 1?
Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?
nJuicy Juice manufactures different juices made entirely of various exotic nuts. Their primary market is China and they operate 3 plants located in Ethiopia, Tanzania and Nigeria. You have been asked to help them determine where to manufacture the two newest juices they offer, Gingko Nut and Kola Nut. Each plant has a different variable cost structure and capacity for manufacturing the different juices. Also each juice has an expected demand. Cost/unit Gingko Kola Ethiopia ¥21.00 ¥22.50 Tanzania ¥22.50 ¥24.50 Nigeria ¥23.00 ¥25.50 Capacity Units/month Ethiopia 425 Tanzania 400 Nigeria 750 Demand Units/month Gingko 550 Kola 450 same exampe is used but in this case each plant has a different fixed and variable cost structur and cpacity for manufacturing the differnt Juices. the fixed cost only applies if the plant produces any juice Capacity Unit-Month Fixed…
nJuicy Juice manufactures different juices made entirely of various exotic nuts. Their primary market is China and they operate 3 plants located in Ethiopia, Tanzania and Nigeria. You have been asked to help them determine where to manufacture the two newest juices they offer, Gingko Nut and Kola Nut. Each plant has a different variable cost structure and capacity for manufacturing the different juices. Also each juice has an expected demand. Cost/unit Gingko Kola Ethiopia ¥21.00 ¥22.50 Tanzania ¥22.50 ¥24.50 Nigeria ¥23.00 ¥25.50 Capacity Units/month Ethiopia 425 Tanzania 400 Nigeria 750 Demand Units/month Gingko 550 Kola 450 How much of each juice should be made at each plant in order to minimize total cost while meeting demand and adhering to plant capacity?
Formulate an LP model for the following problems.1. Bernadette intends to invest up to ₱50,000 in either Best Fund, or a time deposit orboth. The Best Fund pays 8% per year and the time deposit pays 9%. Because theBest Fund is riskier than the time deposit, so she intends to put at most ₱30,000 intothe time deposit and at least ₱10,000 into the Best Fund. How much should she allotto each investment in order to maximize her returns?
I need a detailed explanation and assistance to solve this problem: FruitNuts is a store that sells a variety of unpackaged dried fruit and nut items. The current amounts of supplies of each item are listed in the following table: Item Supply (pounds) dried bananas 800 dried apricots 600 coconut pieces 500 raisins 700 walnuts 900 In addition to the individual items above, the store also sells two kinds of mix products: A Trail Mix product which consists of equal parts of all individual items above A Subway Mix product which consists of two parts walnuts and one part each of the dried bananas, raisins, and coconut pieces. To speed up service, the manager decides to package some of the merchandise in boxes ahead of time. Packaging and price data on boxes are shown below: Packaged Product Weight/Box (pounds) Price/Box ($) Trail Mix 2 7.00 Subway Mix 1 3.00 Dried Bananas 1 2.80 Dried Apricots 1 3.25…
A goldsmith makes two types of jewelry. A model A ring is made with 1 g of gold and 1.5 g of silver and sells for 25 UM.Another model B ring sells for 30 UM and is made of 1.5 g of gold and 1 g of silver. If you only have 750 gof each metal, how many rings should be made of each type to obtain maximum profit?Requested:- Make Initial Table of the problem.- Obtain the Case Variables- Obtain the Objective Function- Get Restrictions- Create the Simplex Table- Obtain the Optimal Solution and the Slack Variables.Solve this operational research exercise.
In aggregate planning models, we can model backlogging of demand by allowing a month's inventory to be negative. a. True b. False . Suppose the allowable increase and decrease for an objective coefficient of a decision variable that has a current value of $50 are $25 (increase) and $10 (decrease). If the coefficient were to change from $50 to $65, the optimal value of the objective function would not change. a. True b. False Shadow prices are associated with binding constraints and show the change in the optimal objective function value when the right side of the constraint equation changes by one unit. a. True b. False In a general logistics model that minimizes the cost of network flow, the flow balance constraint for each supply node has the form a. Flow in ≥ Flow out + Net supply b. Flow out ≥ Flow in + Net demand c. Flow in = Flow out d. Flow out ≤ Flow in +…
A poultry farmer in Lufyanyama has obtained a loan from the Bank to boost his poultry business. He provides you with data to help him optimize the sales. The data is that Old hens can be bought for K20 each but young one cost K50 each. The old hens lay 30 eggs per week, and young ones 50 eggs per week, each egg being worth 30ngwee. A hen cost K10 per week to feed. If a person has only K800 to spend on hens, how many of each kind should he buy to get a profit of more than K600 per week assuming that he cannot house more than 200 hens? a) Formulate the problem as a linear programming model b) Using the Big M – method, how many hens should he buy of each kind to maximize the profit per week? c) Identify the binding and non-binding constraints and justify your choice
Rosa is joining a fundraising event next month to help raise awareness about cancer. She contacted her friend, Tiffany, an artisan who makes customized silver bracelets. Rosa only wants to sell 3 designs: Pink Ribbons, Silver Infinity, and Magenta Hearts. Tiffany estimated that each bracelet will need some amount of silver and a mold. She also needs to shape, carve, and sand the bracelets. Tiffany's profits for each bracelet design are as follows: Pink Ribbons - $2.50, Silver Infinity - $1.50, and Magenta Hearts - $2.00. To make the Pink Ribbons design, Tiffany needs 0.50 pounds of silver and spend 0.25 hours to shape, carve, and sand the bracelets. For the Silver Infinity design, she will need 0.333 pounds of silver and 0.333 hours to shape, carve and sand it. Finally, to produce the Magenta Hearts design, she needs 0.25 pounds of silver and 0.75 hours to shape, carve, and sand it. Rosa was worried that Tiffany will not be able to finish the bracelets in time. Tiffany said not to…
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