You work for the Brad's Nailer Company which manufactures two types of nailers: a pneumatic model and a cordlessmodel. You have contracted to supply a national retail chain with both pneumatic nailers and cordless nailers; theminimum number of nailers is given below. However, Brad's nailer production capability is limited in three departments:production, testing, and packaging. To minimize your costs, you have determined to ship more cordless nailers thanpneumatic. (The number of nailers must be a whole number.)Your answer will be the production hours needed to execute your production plan - rounded to the nearest whole hour.Use Scenario 3Pneum. CostPneum. Prod HrsPneum. Test HrsPneum. Pkg HrsPneum. SalesCordless CostCordless Prod HrsCordless Test HrsCordless Pkg HrsCordless SalesProd Hrs maxTesting Hrs maxPkg Hrs maxScenario 1520.20.30.122,000470.30.40.115,50013,00017,0004,500Scenario 2 Scenario 3 Scenario 455.500.40.30.124,50069.750.30.50.115,50020,00021,0005,50038.500.250.40.118,000340.40.40.214,00021,50018,0005,50079.4.25.157,50052.4.3.15,00020,00017,0005,500

Let 'P' be pneumatic nailers to be produced, and let 'C' be the cordless nailers to be produced. Min…

Answered: You work for the Brad's Nailer Company…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 107P

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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.)
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