2. The Farmer's Hardware and Feed Store is putting together a fertilizer mix for a farmer who is preparing a field to plant a crop. The store will use two brands of fertilizer, Gr-Plus and Crop-Fast, to make the proper mix for the farmer. Each brand yields a specific amount of nitrogen and phosphate as follows: Chemical Contribution Brand Nitrogen (lb/bag) Phosphate (lb/bag) Gro-Plus 2 Crop-Fast 4 4 3 The farmer's field requires at least 16 pounds of Nitrogen and 24 pounds of phosphate. Gro-Plus costs $6 per bag and Crop- Fast costs $3. The store wats to know how many bags of each brand to purchase to minimize the total cost of fertilizing.

2. The Farmer's Hardware and Feed Store is putting together a fertilizer mix for a farmer who is preparing a field to plant a crop. The store will use two brands of fertilizer, Gr-Plus and Crop-Fast, to make the proper mix for the farmer. Each brand yields a specific amount of nitrogen and phosphate as follows: Chemical Contribution Brand Nitrogen (lb/bag) Phosphate (lb/bag) Gro-Plus 2 Crop-Fast 4 4 3 The farmer's field requires at least 16 pounds of Nitrogen and 24 pounds of phosphate. Gro-Plus costs $6 per bag and Crop- Fast costs $3. The store wats to know how many bags of each brand to purchase to minimize the total cost of fertilizing.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 133P

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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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