10. A grocery store sells boxes of cereal. The grocery store sells 48 boxes per day, assume 365 days per year. Boxes cost the store $1.00 each at wholesale costs: theholding cost per item per year is estimated to be 12% of the wholesale cost to buy the goods. Each time the grocery store orders more boxes of cereal, they must payan addifional shipping and handling charge of $150. How many boxes of cereal should the company order in order to minimize their annual ordering and holding costs?

Ordering cost is the cost incurred during the ordering and processing of the product to a supplier.…

Answered: A grocery store sels boxes of cereal.…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter10: Introduction To Simulation Modeling

Section10.4: Simulation With Built-in Excel Tools

Problem 13P

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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?
In the lawn mower production problem in Example 8.4, experiment with the penalty cost for unsatisfied pickups in week 1. If this cost is sufficiently small, does the company ever produce fewer than seven models in week 1 and allow some week 1 pickups to be unsatisfied?
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.)
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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%.
VITRAN Bus Services purchases diesel fuel from Domino Gas Supply. In addition to fuel cost, Domino Gas Supply charges VITRAN Bus Services $250 per order to cover the expenses of delivering and transferring the fuel to VITRAN Bus Services storage tanks. The lead time for new shipment from Domino Gas Supply is 10 days, the cost of holding a gallon of fuel in the storage tanks is $0.04 per month, or $0.48 per year and the annual usage of fuel is 150,000 gallons. VITRAN Bus Services buses operate 300 days a year. What is the optimal order quantity for VITRAN Bus Services? How frequently should VITRAN Bus Services order to replenish the gasoline supply?
The poultry farmer decided to make his own chicken scratch by combining alfalfa and corn in rail car quantities. A rail car of corn costs $400 and a rail car of alfalfa costs $200. The farmer's chickens have a minimum daily requirement of vitamin K (500 milligrams) and iron (400 milligrams), but it doesn't matter whether those elements come from corn, alfalfa, or some other grain. A unit of corn contains 150 milligrams of vitamin K and 75 milligrams of iron. A unit of alfalfa contains 250 milligrams of vitamin K and 50 milligrams of iron. Formulate the linear programming model for this situation. Group of answer choices Min Z = $450C + $200A Subject to: 150C + 250A ≥ 500 75C + 50A ≥ 400 C, A ≥ 0 Min Z = $400C + $200A Subject to: 150C + 250A ≥ 500 75C + 50A ≥ 400 C, A ≥ 0 Max Z = $400C + $500A Subject to: 150C + 250A ≥ 500 75C + 50A ≥ 400 C, A ≥ 0 Max Z = $400C + $200A Subject to: 150C + 250A ≥ 500 75C + 50A ≥ 400 C, A ≥ 0 Min Z = $400C + $200A Subject to: 150C + 250A ≥ 400…
Assume the demand for a company’s 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 soldfor $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.
A retired couple supplement their income by making fruit pies, which they sell to a local grocery store. During the month of September, they produce apple and grape pies. The apple pies are sold for $10.00 to the grocer, and the grape pies are sold for $8.00. The couple is able to sell all of the pies they produce owing to their high quality. They use fresh ingredients. Flour and sugar are purchased once each month. For the month of September, they have 1,500 cups of sugar and 2,400 cups of flour. Each apple pie requires 1½ cups of sugar and 3 cups of flour, and each grape pie requires 2 cups of sugar and 3 cups of flour. a. Determine the number of grape and the number of apple pies that will maximize revenues if the couple working together can make an apple pie in 6 minutes and a grape pie in 3 minutes. They plan to work no more than 60 hours. (Round your answers to nearest whole number.) b. Determine the amounts of sugar, flour, and time that will be unused. (Leave no cells blank -…
The catering manager of LaVista Hotel, Lisa Ferguson, is disturbed by the amount of silverware she is losing every week. Last Friday night, when her crew tried to set up for a banquet for 500 people, they did not have enough knives. She decides she needs to order some more silverware, but wants to take advantage of any quantity discounts her vendor will offer. ≻For a small order (2,000 pieces or less) her vendor quotes a price of $1.80/piece. ≻If she orders 2,001 to 5,000 pieces, the price drops to $1.60/piece. ≻5,001 to 10,000 pieces brings the price to $1.40/piece, and ≻10,001 and above reduces the price to $1.25/piece. Lisa's order costs are $205 per order, her annual holding costs are 5%, and the annual demand is 45,100 pieces. For the best option (the best option is the price level that results in an EOQ within the acceptable range): Part 2 a) What is the optimum ordering quantity? enter your response here units (round your response to the…
The catering manager of LaVista Hotel, Lisa Ferguson, is disturbed by the amount of silverware she is losing every week. Last Friday night, when her crew tried to set up for a banquet for 500 people, they did not have enough knives. She decides she needs to order some more silverware, but wants to take advantage of any quantity discounts her vendor will offer. ≻For a small order (2,000 pieces or less) her vendor quotes a price of $1.80/piece. ≻If she orders 2,001 to 5,000 pieces, the price drops to $1.60/piece. ≻5,001 to 10,000 pieces brings the price to $1.40/piece, and ≻10,001 and above reduces the price to $1.25/piece. Lisa's order costs are $200.00 per order, her annual holding costs are 5%, and the annual demand is 15,000 pieces. For the best option (the best option is the price level that results in an EOQ within the acceptable range): Part 2 a) What is the optimum ordering quantity? ________ units (round your response to the nearest whole…

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