Target is considering opening mini-Target stores in airports across the United States. Target knows that 25% of the items in its store account for 70% of the store's sales and expects that this Pareto relationship will hold for the mini-Target stores. The mini-Targets will each carry 50 items, but it's unknown at this point which 50 items will be stocked. The annual sales of a mini-Target is forecasted to be $500,000. Assume A items are top 20% of items sold, B items are the next 30% and C items are the bottom 50% of items sold. Turnover is expected to be for A items = 50, B items = 40 and C items = 10. 1. The top 20% of items in the min-Target store will account for what percent of sales? - 42.9% - 56.2% - 68.7% - 63.6% 2. What is the annual item sales expected to be for the 25th best selling product in the mini-Target store? - $113 - $4,510 - $437,500 - $76,350

Target is considering opening mini-Target stores in airports across the United States. Target knows that 25% of the items in its store account for 70% of the store's sales and expects that this Pareto relationship will hold for the mini-Target stores. The mini-Targets will each carry 50 items, but it's unknown at this point which 50 items will be stocked. The annual sales of a mini-Target is forecasted to be $500,000. Assume A items are top 20% of items sold, B items are the next 30% and C items are the bottom 50% of items sold. Turnover is expected to be for A items = 50, B items = 40 and C items = 10. 1. The top 20% of items in the min-Target store will account for what percent of sales? - 42.9% - 56.2% - 68.7% - 63.6% 2. What is the annual item sales expected to be for the 25th best selling product in the mini-Target store? - $113 - $4,510 - $437,500 - $76,350

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 97P

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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. 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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