A food processor uses about 11,250 pounds of wheat each week. The food processor estimates theirholding cost to be 30% per year. A supplier has offered the food processor two options. Option 1 is topurchase wheat in lots of 35,000 pounds (truckload). The price per pound for option 1 is $1.2 per pound.Option 2 is to have wheat delivered by rail. The cost per pound for option 2 would be $1 per pound.Deliveries by rail will include 150,000 pounds of wheat. In either case, the supplier will charge the firm afixed fee of $250 per delivery.Round your answer to two decimal places.What is the total annual (52 week) holding and ordering cost of option 2?dollars

Given data Weekly demand = 11250 pounds of wheat Week in a year 52. Hence, annual demand or total…

Answered: A food processor uses about 11,250…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 49P: If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60...

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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?
If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.
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. Can you guess the results of a sensitivity analysis on the initial inventory in the Pigskin model? See if your guess is correct by using SolverTable and allowing the initial inventory to vary from 0 to 10,000 in increments of 1000. Keep track of the values in the decision variable cells and the objective cell.
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?
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.
Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?
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
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?
Ford has four automobile plants. Each is capable of producing the Taurus, Lincoln or Escort but it an only produce one of these cars. The fixed cost of operating each plant for a year and the variable cost of producing a car of each type at the plant are in the table. Variable Cost $ Plant Fixed Cost $ Taurus Lincoln Escort 1 7 billion 12,000 16,000 9,000 2 6 billion 15,000 18,000 11,000 3 4 billion 17,000 19,000 12,000 4 2 billion 19,000 22,000 14,000 Ford faces the following restrictions: each plant can produce only one type of car the total production of each type of car must be at a single plant; that is for examply if any Tauruses are made at plant 1, then all Tauruses must be made there if plants 3 and 4 are used then plant 1 must also be used Each year, Ford must produce 500,000 of each type of car. Question: Formulate an IP whose solution will tell Ford how to minimize the annual cost of producing cars.
1. At the beginning of each semester, BOOKY can order 60, 80, or 100 copies of the book from the publisher, each with differing discounts per book. The ordering costs are listed in the following table. Number of Books Ordered 60 80 100 Ordering Costs 6100 7700 9100 2. BOOKY can either sell the book at the retail price ($130 per copy) or offer a 10% discount ($117 per copy). The demand distributions under different selling prices are listed in the following tables. The demand distribution for the textbook when the selling price is $130 per copy. Demand Probability 70 0.6 90 0.4 The demand distribution for the textbook when the selling price is $117 per copy. Demand Probability 80 0.15 100 0.85 3. Any unmet demand for the textbook will be irrecoverable There are two decision variables in this decision problem: the ordering quantity and the selling price of the textbook. a) If BOOKY is allowed to return unsold textbooks to the publisher for a refund of…

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